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University of Texas – Austin
1.
Dumav, Martin.
The von Neumann/Morgenstern approach to ambiguity.
Degree: MA, Mathematics, 2011, University of Texas – Austin
URL: http://hdl.handle.net/2152/ETD-UT-2011-08-4292
► An outcome is ambiguous if it is an incomplete description of the probability distribution over consequences. An `incomplete description' is identified with the set of…
(more)
▼ An outcome is ambiguous if it is an incomplete description of the probability distribution over consequences. An `incomplete description' is identified with the set of probabilities that satisfy the incomplete description. A choice problem is uncertain if the decision maker is choosing between distributions, and is ambiguous if the decision maker is choosing between sets of probabilities. The von Neumann/Morgenstern approach to uncertain choice problems uses a continuous linear function on probabilities. This paper develops the theory of ambiguous choice problems as a continuous, linear functions on closed convex sets of probabilities. This delivers: a framework encompassing most of the extant ambiguity averse preferences; a complete separation of attitudes towards risk and attitudes toward ambiguity; and generalizations of rst and second order stochastic dominance rankings to ambiguous decision problem. Quasi-concave preferences on sets that satisfy a restricted betweenness property capture variational preferences.
Advisors/Committee Members: Ẑitković, Gordan (advisor), Sirbu, Mihai (committee member).
Subjects/Keywords: Ambiguity; Decision theory; von Neumann/Morgenstern
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APA (6th Edition):
Dumav, M. (2011). The von Neumann/Morgenstern approach to ambiguity. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2011-08-4292
Chicago Manual of Style (16th Edition):
Dumav, Martin. “The von Neumann/Morgenstern approach to ambiguity.” 2011. Masters Thesis, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/ETD-UT-2011-08-4292.
MLA Handbook (7th Edition):
Dumav, Martin. “The von Neumann/Morgenstern approach to ambiguity.” 2011. Web. 16 Apr 2021.
Vancouver:
Dumav M. The von Neumann/Morgenstern approach to ambiguity. [Internet] [Masters thesis]. University of Texas – Austin; 2011. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4292.
Council of Science Editors:
Dumav M. The von Neumann/Morgenstern approach to ambiguity. [Masters Thesis]. University of Texas – Austin; 2011. Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4292

University of Texas – Austin
2.
Goswami, Pulak.
Recovering the payoff structure of a utility maximizing agent.
Degree: PhD, Mathematics, 2016, University of Texas – Austin
URL: http://hdl.handle.net/2152/40299
► Any agent with access to information that is not available to the market at large is considered an ‘insider’. It is possible to interpret the…
(more)
▼ Any agent with access to information that is not available to the market at large is considered an ‘insider’. It is possible to interpret the effect of this private information as change in the insider’s probability measure. In the case of exponential utility, logarithm of the Radon-Nikodym derivative for the change in measure will appear as a random endowment in the objective the insider would maximize with respect to the original measure. The goal of this paper is to find conditions under which it is possible to recover the structure of this random endowment given only a single trajectory of his/her wealth. To do this, it is assumed that the random endowment is a function of the terminal value of the state variable and that the market is complete.
Advisors/Committee Members: Žitković, Gordan (advisor), Sirbu, Mihai (committee member), Pavlovic, Natasa (committee member), Larsen, Kasper (committee member).
Subjects/Keywords: Inverse problems; Insider trading
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APA (6th Edition):
Goswami, P. (2016). Recovering the payoff structure of a utility maximizing agent. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/40299
Chicago Manual of Style (16th Edition):
Goswami, Pulak. “Recovering the payoff structure of a utility maximizing agent.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/40299.
MLA Handbook (7th Edition):
Goswami, Pulak. “Recovering the payoff structure of a utility maximizing agent.” 2016. Web. 16 Apr 2021.
Vancouver:
Goswami P. Recovering the payoff structure of a utility maximizing agent. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/40299.
Council of Science Editors:
Goswami P. Recovering the payoff structure of a utility maximizing agent. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/40299

University of Texas – Austin
3.
Fayvisovich, Roman.
Martingale-generated control structures and a framework for the dynamic programming principle.
Degree: PhD, Mathematics, 2017, University of Texas – Austin
URL: http://hdl.handle.net/2152/62105
► This thesis constructs an abstract framework in which the dynamic programming principle (DPP) can be proven for a broad range of stochastic control problems. Using…
(more)
▼ This thesis constructs an abstract framework in which the dynamic
programming principle (DPP) can be proven for a broad range of stochastic
control problems. Using a distributional formulation of stochastic control, we
prove the DPP for problems that optimize over sets of martingale measures. As
an application, we use the classical martingale problem to prove the DPP for
weak solutions of controlled diffusions, and use it show that the value function
is a viscosity solution of the associated Hamilton-Jacobi-Bellman equation.
Advisors/Committee Members: Žitković, Gordan (advisor), Sirbu, Mihai (committee member), Zariphopoulou, Thaleia (committee member), Larsen, Kasper (committee member).
Subjects/Keywords: Stochastic control; Dynamic programming
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Fayvisovich, R. (2017). Martingale-generated control structures and a framework for the dynamic programming principle. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/62105
Chicago Manual of Style (16th Edition):
Fayvisovich, Roman. “Martingale-generated control structures and a framework for the dynamic programming principle.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/62105.
MLA Handbook (7th Edition):
Fayvisovich, Roman. “Martingale-generated control structures and a framework for the dynamic programming principle.” 2017. Web. 16 Apr 2021.
Vancouver:
Fayvisovich R. Martingale-generated control structures and a framework for the dynamic programming principle. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/62105.
Council of Science Editors:
Fayvisovich R. Martingale-generated control structures and a framework for the dynamic programming principle. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/62105
4.
Wang, Haoran, Ph. D.
Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation.
Degree: PhD, Mathematics, 2019, University of Texas – Austin
URL: http://dx.doi.org/10.26153/tsw/2836
► The goal of this thesis is to introduce a new, alternative approach to deal with model uncertainty and “real-time” model revisions and, in turn, develop…
(more)
▼ The goal of this thesis is to introduce a new, alternative approach to deal with model uncertainty and “real-time” model revisions and, in turn, develop a comparative study with existing approaches in the context of various applications in financial mathematics. This new approach is based on the forward performance criteria which adapt in a time-consistent way to “real-time” model revisions. The novelty is that these revisions are genuinely “model-free” in that they occur in “real-time”, without any modeling pre-commitment. For example, in the context of optimal liquidation (see Chapter 3 and Chapter 4), there is no a priori model for the evolution of the market impact parameter λ. It is rather assumed that this parameter switches at predictable times, to values only observable at the switching times. As such, the model revisions capture the evolving reality and allow for considerable flexibility. This forward approach thus incorporates “real-time” model revisions and is, therefore, close to adaptive optimization. On the other hand, it produces, by construction, time-consistent policies and is, thus, close to the classical optimization with model(s) pre-commitment. In other words, it can be thought as a hybrid approach that accommodates dynamic model changes while preserving time-consistency. We apply the forward approach with “real-time” model revisions in four distinct problems: portfolio management in discrete and continuous settings (binomial and lognormal, respectively), indifference valuation in lognormal models and optimal liquidation in the continuous time Almgren-Chriss model. We produce closed form solutions and characterize the optimal policies and optimal criteria. As the analysis shows, one needs to solve various sequential “inverse” optimal investment problems with random coefficients, corresponding to model revisions in real-time. We develop a comparative study with the classical settings. A main novelty is the introduction of two performance metrics which measure the discrepancies between the actual performance, and the projected or the true optimal performances under the various criteria and behavior. We study these metrics for various scenaria, related to favorable and non-favorable market changes, and compare their performance. These metrics resemble the notion of “regret”, which is now considered in a more dynamic and “real-time” manner. Among others, we show that the regret of the forward decision maker is always zero, independently of the upcoming model changes. In what follows, we describe each application separately. For each application, we introduce the model, the forward and classical criteria, construct the corresponding solutions and policies, and compare them in detail
Advisors/Committee Members: Zariphopoulou, Thaleia, 1962- (advisor), Sirbu, Mihai (committee member), Zitkovic, Gordan (committee member), Muthuraman, Kumar (committee member).
Subjects/Keywords: Forward performance processes; Optimal control; Adaptive control; Time consistency; Regret; Real-time model adaptation; Portfolio management; Indifference valuation; Optimal liquidation
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Wang, Haoran, P. D. (2019). Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/2836
Chicago Manual of Style (16th Edition):
Wang, Haoran, Ph D. “Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://dx.doi.org/10.26153/tsw/2836.
MLA Handbook (7th Edition):
Wang, Haoran, Ph D. “Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation.” 2019. Web. 16 Apr 2021.
Vancouver:
Wang, Haoran PD. Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Apr 16].
Available from: http://dx.doi.org/10.26153/tsw/2836.
Council of Science Editors:
Wang, Haoran PD. Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/2836
5.
-5991-6641.
Modeling and analyzing device-to-device content distribution in cellular networks.
Degree: PhD, Electrical and Computer Engineering, 2017, University of Texas – Austin
URL: http://hdl.handle.net/2152/67991
► Device-to-device (D2D) communication is a promising approach to optimize the utilization of air interface resources in 5G networks, since it allows decentralized proximity-based communication. To…
(more)
▼ Device-to-device (D2D) communication is a promising approach to optimize the utilization of air interface resources in 5G networks, since it allows decentralized proximity-based communication. To obtain caching gains through D2D, mobile nodes must possess content that other mobiles want. Thus, devising intelligent cache placement techniques are essential for D2D. The goal of this dissertation is to provide randomized spatial models for content distribution in cellular networks by capturing the locality of the content, and additionally, to provide dynamic content placement algorithms exploiting the node configurations.
First, a randomized content caching scheme for D2D networks in the cellular context is proposed. Modeling the locations of the devices as a homogeneous Poisson Point Process (PPP), the probability of successful content delivery in the presence of interference and noise is derived. With some idealized modeling aspects, i.e., given that (i) only a fraction of users to be randomly scheduled at a given time, and (ii) the request distribution does not change over time, it has been shown that the performance of caching can be optimized by smoothing out the request distribution, where the smoothness of the caching distribution is mainly determined by the path loss exponent, and holds under Rayleigh, Ricean and Nakagami fading models.
Second, to take the randomized caching model a step further, a spatially correlated content caching scenario is contemplated. Inspired by the Matérn hard-core point process of type II, which is a first-order pairwise interaction model, D2D nodes caching the same file are never closer to each other than the exclusion radius. The exclusion radius plays the role of a substitute for caching probability. The optimal exclusion radii that maximize the hit probability can be determined by using the request distribution and cache memory size. Unlike independent content placement, which is oblivious to the geographic locations of the nodes, the new strategy can be effective for proximity-based communication even when the cache size is small.
Third, an auction-aided Matérn carrier sense multiple access (CSMA) policy that considers the joint analysis of scheduling and caching is studied. The auction scheme is distributed. Given a cache configuration, i.e., the set of cached files in each user at a given snapshot, each D2D receiver determines the value of its request, by bidding on the set of potential transmitters in its communication range. The values of the receiver bids are reported to the potential transmitter, which computes the cumulated sum of these variables taken on all users in its cell. The potential transmitter then reports the value of the bid sum to other potential transmitters in its contention range. Given the accumulated bids of all potential transmitters, the contention range and the medium access probability, a fraction of the potential transmitters are jointly scheduled, determined by the auction policy, in order to optimize the throughput. Later, a Gibbs…
Advisors/Committee Members: Andrews, Jeffrey G. (advisor), Baccelli, Francois (committee member), de Veciana, Gustavo (committee member), Dimakis, Alexandros G. (committee member), Sirbu, Mihai (committee member).
Subjects/Keywords: Content distribution; Caching; Device-to-device; Spatial diversity
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
-5991-6641. (2017). Modeling and analyzing device-to-device content distribution in cellular networks. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/67991
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Chicago Manual of Style (16th Edition):
-5991-6641. “Modeling and analyzing device-to-device content distribution in cellular networks.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/67991.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
MLA Handbook (7th Edition):
-5991-6641. “Modeling and analyzing device-to-device content distribution in cellular networks.” 2017. Web. 16 Apr 2021.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
-5991-6641. Modeling and analyzing device-to-device content distribution in cellular networks. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/67991.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Council of Science Editors:
-5991-6641. Modeling and analyzing device-to-device content distribution in cellular networks. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/67991
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
6.
-9740-0742.
Applications of forward performance processes in dynamic optimal portfolio management.
Degree: PhD, Information, Risk, and Operations Management, 2018, University of Texas – Austin
URL: http://hdl.handle.net/2152/63813
► The classical optimal investment models are cast in a finite or infinite horizon setting, assuming an a priori choice of a market model (or a…
(more)
▼ The classical optimal investment models are cast in a finite or infinite horizon setting, assuming an a priori choice of a market model (or a family of models) as well as a priori choice of a utility function of terminal wealth and/or intermediate consumption. Once these choices are made, namely, the horizon, the model and the risk preferences, stochastic optimization technique yield the maximal expected utility (value function) and the optimal policies wither through the Hamilton-Jacobi-Bellman equation in Makovian models or, more generally, via duality in semi-martingale models. A fundamental property of the solution is time-consistency, which follows from the Dynamic Programming Principle (DPP). This principle provides the intuitively pleasing interpretation of the value function as the intermediate (indirect) utility. It also states that the value function is a martingale along the optimal wealth trajectory and a super-martingale along every admissible one. These properties provide a time-consistent framework of the solutions, which ``pastes" naturally one investment period to the next.
Despite its mathematical sophistication, the classical expected utility framework cannot accommodate model revision, nor horizon flexibility nor adaptation of risk preferences, if one desires to retain time-consistency. Indeed, the classical formulation is by nature ``backwards" in time and, thus, it does not allow any ``forward in time" changes. For example, on-line learning, which typically occurs in a non-anticipated way, cannot be implemented in the classical setting, simply because the latter evolves backwards while the former progresses forward in time.
To alleviate some of these limitations while, at the same time, preserving the time-consistency property, Musiela and Zariphopoulou proposed an alternative criterion, the so-called forward performance process. This process satisfies the DPP forward in time, and generalizes the classical expected utility. For a large family of cases, forward performance processes have been explicitly constructed for general Ito-diffusion markets. While there has already been substantial mathematical work on this criterion, concrete applications to applied portfolio management are lacking.
In this thesis, the aim is to focus on applied aspects of the forward performance approach and build meaningful connections with practical portfolio management. The following topics are being studied.
Chapter 2 starts with providing an intuitive characterization of the underlying performance measure and the associated risk tolerance process, which are the most fundamental ingredients of the forward approach. It also provides a novel decomposition of the initial condition and, in turn, its inter-temporal preservation as the market evolves. The main steps involve a system of stochastic differential equations modeling various stochastic sensitivities and risk metrics.
Chapter 3 focuses on the applications of the above results to lifecycle portfolio management. Investors are firstly classified by their…
Advisors/Committee Members: Zariphopoulou, Thaleia, 1962- (advisor), Carvalho, Carlos (committee member), Muthuraman, Kumar (committee member), Tompaidis, Stathis (committee member), Sirbu, Mihai (committee member).
Subjects/Keywords: Forward performance; Portfolio optimization; Lifecycle fund; Mean-variance analysis
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
-9740-0742. (2018). Applications of forward performance processes in dynamic optimal portfolio management. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/63813
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Chicago Manual of Style (16th Edition):
-9740-0742. “Applications of forward performance processes in dynamic optimal portfolio management.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/63813.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
MLA Handbook (7th Edition):
-9740-0742. “Applications of forward performance processes in dynamic optimal portfolio management.” 2018. Web. 16 Apr 2021.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
-9740-0742. Applications of forward performance processes in dynamic optimal portfolio management. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/63813.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Council of Science Editors:
-9740-0742. Applications of forward performance processes in dynamic optimal portfolio management. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/63813
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin
7.
Geng, Tianran.
Essays on forward portfolio theory and financial time series modeling.
Degree: PhD, Mathematics, 2017, University of Texas – Austin
URL: http://hdl.handle.net/2152/63031
► This dissertation contains four self-contained essays that explore the application of stochastic and statistical modeling techniques to the problem of optimal portfolio choice and financial…
(more)
▼ This dissertation contains four self-contained essays that explore the application of stochastic and statistical modeling techniques to the problem of optimal portfolio choice and financial time series analysis. The first essay presents turnpike-type results for the risk tolerance function in an incomplete Ito-diffusion market setting under time-monotone for- ward performance criteria. We show that, contrary to the classical case, the temporal and spatial limits do not coincide. Rather, we establish that they depend directly on the left- and right-end of the support of an underlying measure, used to construct the forward performance criterion. We provide examples with discrete and continuous measures, and discuss the asymptotic behavior of the risk tolerance for each case. The second essay examines the long term behavior of the optimal wealth and optimal portfolio weights processes in an Ito-diffusion market under the time-monotone forward performance criteria. We show that the underlying measure [mu] associated with the forward performance criterion defines the risk profile of the investor, and in turn determines the optimal portfolio strategy and optimal wealth in the long run. The third essay considers two fund managers who trade under relative performance concerns, depending on each other’s strategies, in an Ito-diffusion market, We analyze both the passive and the competitive cases, and under both asset specialization and diversification. To allow for dynamic model re- vision and flexible investment horizons, we introduce the concept of relative forward performance for the passive case, and the notion of forward Nash equilibrium for the competitive one. For homothetic forward criteria, we provide explicit solutions for all cases. In the fourth essay, we assess the dynamics of realized betas, relative to the dynamics in the underlying market variance and covariances with the market, using 5-minute high-frequency asset prices of the DJIA component stocks from January 1, 2010 to December 31, 2014. We find that, unlike the realized variances and covariances which fluctuate widely and are highly persistence, the realized beta series, on the other hand, display much less persistence. We then construct a simple autoregressive plus noise DLM time series model for the realized beta, where the measurement error follows a normal distribution centered at zero with asymptotically valid variance given in Barndorff-Nielsen & Shepherd (2004). This approach helps us obtain samples from filtered and smoothed true underlying beta series and forecast future betas.
Advisors/Committee Members: Zariphopoulou, Thaleia, 1962- (advisor), Mendoza-Arriaga, Rafael (committee member), Sirbu, Mihai (committee member), Zitkovic, Gordan (committee member), Walker, Stephen (committee member).
Subjects/Keywords: Forward portfolio theory; Time series analysis; Optimal portfolio choice; Mathematical finance
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Geng, T. (2017). Essays on forward portfolio theory and financial time series modeling. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/63031
Chicago Manual of Style (16th Edition):
Geng, Tianran. “Essays on forward portfolio theory and financial time series modeling.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/63031.
MLA Handbook (7th Edition):
Geng, Tianran. “Essays on forward portfolio theory and financial time series modeling.” 2017. Web. 16 Apr 2021.
Vancouver:
Geng T. Essays on forward portfolio theory and financial time series modeling. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/63031.
Council of Science Editors:
Geng T. Essays on forward portfolio theory and financial time series modeling. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/63031

University of Texas – Austin
8.
-0056-8793.
Existence, characterization and approximation in the generalized monotone follower problem.
Degree: PhD, Mathematics, 2015, University of Texas – Austin
URL: http://hdl.handle.net/2152/31517
► We revisit the classical monotone-follower problem and consider it in a generalized formulation. Our approach, based on a compactness substitute for nondecreasing processes, the Meyer-Zheng…
(more)
▼ We revisit the classical monotone-follower problem and consider it in a generalized formulation. Our approach, based on a compactness substitute for nondecreasing processes, the Meyer-Zheng weak convergence, and the maximum principle of Pontryagin, establishes existence under minimal conditions, produces general approximation results and further elucidates the celebrated connection between optimal stochastic control and stopping.
Advisors/Committee Members: Žitković, Gordan (advisor), Chen, Thomas (committee member), Larsen, Kasper (committee member), Sirbu, Mihai (committee member), Zariphopoulou, Thaleia (committee member).
Subjects/Keywords: Maximum principle; Meyer-Zheng convergence; Monotone-follower problem; Optimal stochastic control; Optimal stopping; Singular control
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
-0056-8793. (2015). Existence, characterization and approximation in the generalized monotone follower problem. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31517
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Chicago Manual of Style (16th Edition):
-0056-8793. “Existence, characterization and approximation in the generalized monotone follower problem.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/31517.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
MLA Handbook (7th Edition):
-0056-8793. “Existence, characterization and approximation in the generalized monotone follower problem.” 2015. Web. 16 Apr 2021.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
-0056-8793. Existence, characterization and approximation in the generalized monotone follower problem. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/31517.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Council of Science Editors:
-0056-8793. Existence, characterization and approximation in the generalized monotone follower problem. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/31517
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
9.
Chatterjee, Avhishek.
Understanding dynamics and resource allocation in social networks.
Degree: PhD, Electrical and Computer engineering, 2015, University of Texas – Austin
URL: http://hdl.handle.net/2152/32421
► Widespread popularity of various online social networks has attracted significant attention of the research community. Research interest in social networks are broadly divided into two…
(more)
▼ Widespread popularity of various online social networks has attracted
significant attention of the research community. Research interest
in social networks are broadly divided into two categories:
understanding the social or human network dynamics and harnessing the social network
dynamics to gain economic, business or political advantage using minimal
resource. These two research directions fuel each other.
Better understanding offers better resource utilization/allocation in harnessing
the network and the need for better resource utilization/allocation
drives the fundamental research in understanding
human networks. This thesis considers important problems in both
directions as well as at their intersection.
We first study opinion dynamics in social networks. We propose a new stochastic
dynamics which generalizes two widely used and complementary models of opinion
dynamics, graph-based linear dynamics and bounded confidence dynamics
into a single stochastic dynamics. We analytically study the conditions under which
such dynamics result in reconciliation or some sort of consensus. Our findings
relate well to observed behaviors of societies.
The next problem that we consider is related to designing personalized/targeted
advertisements or campaigns for social network users. Currently viral marketing
or campaigning rely only on the structure of the friendship graph. In reality
friends may have different opinions on different topics or issues. It is understood that
if opinions regarding a topic were known one could design better
targeted campaigns. We propose algorithms which can infer opinions of people
by observing their interactions regarding a topic or an issue. As data
gathering and computation requires resources, our algorithm is designed to
work with fewer such resources for a broad class of social networks and
interaction patterns.
A recent trend among different businesses
is to work with social software providers (e.g., Lithium, Salesforce.com)
to engage consumers online and often involve the online
crowd directly in developing and running business ideas.
This trend, popularly known as crowdsourcing uses human cloud to
do jobs that cannot be done by machines. Crowdsourcing
has been successfully used to do simple human tasks (Amazon Mechanical Turk),
scientific research (fold.it), freelance software development(oDesk) as well
as in impacting the lives of people in poverty (Samasource).
Many big business houses use crowdsourcing, e.g., Microsoft, Samsung, Intel etc.,
IBM harness its employee pool using internal crowdsourcing.
As employing humans (a.k.a. agents) for jobs,
and especially for skilled jobs (like software
development, scientific studies) is costly, an efficient job to agent allocation
is key to the success of crowdsourcing. Motivated by this, in the last part of
the thesis we study efficient resource allocation in skill-based crowdsourcing
platforms.
Advisors/Committee Members: Vishwanath, Sriram (advisor), Baccelli, Francois (committee member), Sanghavi, Sujay (committee member), Shakkottai, Sanjay (committee member), Sirbu, Mihai (committee member), Varshney, Lav (committee member).
Subjects/Keywords: Social networks; Crowdsourcing; Opinion dynamics; Opinion inference
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APA (6th Edition):
Chatterjee, A. (2015). Understanding dynamics and resource allocation in social networks. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32421
Chicago Manual of Style (16th Edition):
Chatterjee, Avhishek. “Understanding dynamics and resource allocation in social networks.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/32421.
MLA Handbook (7th Edition):
Chatterjee, Avhishek. “Understanding dynamics and resource allocation in social networks.” 2015. Web. 16 Apr 2021.
Vancouver:
Chatterjee A. Understanding dynamics and resource allocation in social networks. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/32421.
Council of Science Editors:
Chatterjee A. Understanding dynamics and resource allocation in social networks. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32421

University of Texas – Austin
10.
Choi, Chang-sik.
Modeling and analysis of wireless networks with correlation and motion.
Degree: PhD, Electrical and Computer Engineering, 2019, University of Texas – Austin
URL: http://dx.doi.org/10.26153/tsw/3009
► The use of stochastic geometry allows the analysis of the typical performance of a wireless network. Specifically, under a stationary framework, the network performance at…
(more)
▼ The use of stochastic geometry allows the analysis of the typical performance of a wireless network. Specifically, under a stationary framework, the network performance at a typical receiver represents the network performance spatially-averaged over all receivers. This approach has been applied to the Poisson point processes whose points are independently located in space. The Poisson point process expresses a total independence type randomness in network architectures. Its tractability leads to its wide use in modeling various wireless networks, e.g., cellular networks, ad hoc networks, and vehicular networks.
However, a network analysis using the Poisson point process might be inaccurate when the network components are geometrically correlated or in motion, as in heterogeneous cellular networks, or vehicular networks. For instance, macro base stations are deployed far from each other. Vehicles are located on roads, i.e., lines, and they move on the lines. As a result, the analysis of these networks can be improved by new spatial models that capture these spatial and dynamic features.
In my first contribution, I derive the signal-to-interference ratio (SIR) coverage probability of a typical user in heterogeneous cellular networks where base stations are modeled by the sum of a Poisson point process and a stationary square grid. In my second contribution, I develop a stationary framework based on the sum of a Cox point process and a Poisson point process to model random cellular networks with linear base stations and linear users on straight lines. I derive the SIR coverage probability of the typical user and characterize its association. In the third contribution, I investigate the statistical properties of the Cox point process, exploring the nearest distance distribution and the convergence of the Cox-Voronoi cell. In the above three contributions, I analyze the performance of wireless networks by focusing on their correlated structures, extracting results which cannot be obtained from models based only on Poisson point processes.
In my fourth contribution, I propose a new technology for harvesting Internet-of-Things (IoT) data based on mesh relaying with vehicles as sinks. I derive the network capacity and compare it to the traditional approach, which is based on static base stations. In the fifth contribution, I derive the SIR distribution of direct communication from roadside devices to vehicles. By characterizing the evolution of the network snapshots, I derive the behavior of vehicles' service coverage area and the network latency. In my sixth contribution, I propose a data harvesting technology for the ground-based data devices, based on the use of unmanned aerial vehicles (UAVs). I derive the total data transmitted from a typical device by characterizing the evolution of network geometry with respect to time. These last three contributions are built on a combination of network snapshot analysis and network evolution analysis.
Advisors/Committee Members: Baccelli, F. (François), 1954- (advisor), de Veciana, Gustavo (committee member), Heath, Robert W (committee member), Andrews, Jeffrey G (committee member), Sirbu, Mihai (committee member).
Subjects/Keywords: Stochastic geometry; Wireless networks; Vehicular networks; Modeling and analysis; Point process; Mesh networks; Vehicles
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Choi, C. (2019). Modeling and analysis of wireless networks with correlation and motion. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/3009
Chicago Manual of Style (16th Edition):
Choi, Chang-sik. “Modeling and analysis of wireless networks with correlation and motion.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://dx.doi.org/10.26153/tsw/3009.
MLA Handbook (7th Edition):
Choi, Chang-sik. “Modeling and analysis of wireless networks with correlation and motion.” 2019. Web. 16 Apr 2021.
Vancouver:
Choi C. Modeling and analysis of wireless networks with correlation and motion. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Apr 16].
Available from: http://dx.doi.org/10.26153/tsw/3009.
Council of Science Editors:
Choi C. Modeling and analysis of wireless networks with correlation and motion. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/3009
11.
Duque, Luis Felipe.
The double obstacle problem and the two membranes problem.
Degree: PhD, Mathematics, 2018, University of Texas – Austin
URL: http://hdl.handle.net/2152/68152
► In the first part of this dissertation, we study the existence, regularity and the free boundary of the double obstacle problem in different formulations that…
(more)
▼ In the first part of this dissertation, we study the existence, regularity and the free boundary of the double obstacle problem in different formulations that involve linear, elliptic, parabolic and fully nonlinear equations.
The second part focuses on the two membranes problem for fully nonlinear elliptic operators, here we prove the existence of solutions and then we prove the optimal regularity when the operators involved are the Pucci operators. Finally, we give an example that shows that no regularity for the free boundary is to be expected to hold in general.
Advisors/Committee Members: Caffarelli, Luis A. (advisor), Vasseur, Alexis (committee member), Arapostathis, Aristotle (committee member), Sirbu, Mihai (committee member).
Subjects/Keywords: Differential equations; Free boundary problems; Double membranes problem; Double obstacle problem; Obstacle problem; Regularity
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Duque, L. F. (2018). The double obstacle problem and the two membranes problem. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68152
Chicago Manual of Style (16th Edition):
Duque, Luis Felipe. “The double obstacle problem and the two membranes problem.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/68152.
MLA Handbook (7th Edition):
Duque, Luis Felipe. “The double obstacle problem and the two membranes problem.” 2018. Web. 16 Apr 2021.
Vancouver:
Duque LF. The double obstacle problem and the two membranes problem. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/68152.
Council of Science Editors:
Duque LF. The double obstacle problem and the two membranes problem. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/68152
12.
Choi, Jin Hyuk, 1983-.
A shadow-price approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type.
Degree: PhD, Mathematics, 2012, University of Texas – Austin
URL: http://hdl.handle.net/2152/ETD-UT-2012-08-5926
► We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that…
(more)
▼ We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. By analyzing the properties of the free boundary problem, we provide an explicit characterization of model parameters for which the value function is finite. Furthermore, we prove that the value function, as well as the slopes of the lines demarcating the no-trading region, can be expanded as a series of integer powers of [lambda superscript 1/3]. The coefficients of arbitrary order in this expansion can be computed.
Advisors/Committee Members: Žitković, Gordan (advisor), Sirbu, Mihai (advisor), Larsen, Kasper (committee member), Tompaidis, Stathis (committee member), Zariphopoulou, Thaleia (committee member).
Subjects/Keywords: Optimal consumption; Singular stochastic control; Transaction costs; Shadow prices
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Choi, Jin Hyuk, 1. (2012). A shadow-price approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-08-5926
Chicago Manual of Style (16th Edition):
Choi, Jin Hyuk, 1983-. “A shadow-price approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/ETD-UT-2012-08-5926.
MLA Handbook (7th Edition):
Choi, Jin Hyuk, 1983-. “A shadow-price approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type.” 2012. Web. 16 Apr 2021.
Vancouver:
Choi, Jin Hyuk 1. A shadow-price approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-5926.
Council of Science Editors:
Choi, Jin Hyuk 1. A shadow-price approach of the problem of optimal investment/consumption with proportional transaction costs and utilities of power type. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-5926
13.
White, Christopher Dale.
Optimality guarantees for non-convex low rank matrix recovery problems.
Degree: PhD, Mathematics, 2015, University of Texas – Austin
URL: http://hdl.handle.net/2152/32534
► Low rank matrices lie at the heart of many techniques in scientific computing and machine learning. In this thesis, we examine various scenarios in which…
(more)
▼ Low rank matrices lie at the heart of many techniques in scientific computing and machine learning. In this thesis, we examine various scenarios in which we seek to recover an underlying low rank matrix from compressed or noisy measurements. Specifically, we consider the recovery of a rank r positive semidefinite matrix XX[superscript T] ∈ R[superscript n x n] from m scalar measurements of the form [mathematic equation] via minimization of the natural l₂ loss function [mathematic equation]; we also analyze the quadratic nonnegative matrix factorization (QNMF) approach to clustering where the matrix to be factorized is the transition matrix for a reversible Markov chain. In all of these instances, the optimization problem we wish to solve has many local optima and is highly non-convex. Instead of analyzing convex relaxations, which tend to be complicated and computationally expensive, we operate directly on the natural non-convex problems and prove both local and global optimality guarantees for a family of algorithms.
Advisors/Committee Members: Ward, Rachel A. (advisor), Baccelli, Francois (committee member), Osting, Braxton (committee member), Sanghavi, Sujay (committee member), Sirbu, Mihai (committee member), Zitkovic, Gordan (committee member).
Subjects/Keywords: Optimization; Non-convex; Low rank matrix
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
White, C. D. (2015). Optimality guarantees for non-convex low rank matrix recovery problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32534
Chicago Manual of Style (16th Edition):
White, Christopher Dale. “Optimality guarantees for non-convex low rank matrix recovery problems.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://hdl.handle.net/2152/32534.
MLA Handbook (7th Edition):
White, Christopher Dale. “Optimality guarantees for non-convex low rank matrix recovery problems.” 2015. Web. 16 Apr 2021.
Vancouver:
White CD. Optimality guarantees for non-convex low rank matrix recovery problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2152/32534.
Council of Science Editors:
White CD. Optimality guarantees for non-convex low rank matrix recovery problems. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32534
.