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You searched for subject:(Exponential Brownian functional). Showing records 1 – 2 of 2 total matches.

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1. Yang, Fenghao. On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems.

Degree: PhD, Mathematics & Statistics, 2018, York University

A new class of exponential functionals arises when pricing certain equity-linked insurance products.We study the distribution of these exponential functionals using tools from Probability and Complex Analysis. In the case of the Kou process we obtain an explicit formula for the probability density function of the exponential functional and we apply this result to pricing equity-linked insurance products. As a by-product of this research we have also derived a new class of duality relations for hypergeometric functions. In the second part of the thesis, we study correlation uncertainty in Credit Risk. The goal is to price analogues of first-to-default options under the assumption that the assets follow correlated stochastic processes with known marginal distributions and unknown dependence structure. We solve this problem using tools from Stochastic Analysis and Optimal Control Theory. We provide explicit solutions in some specific examples and numerical approximations in the more general case. Advisors/Committee Members: Salisbury, Thomas (advisor), Kuznetsov, Alexey (advisor).

Subjects/Keywords: Finance; Levy processes; Kou processes; General exponential functional; Skew Brownian motion; Asymmetric local time; Mellin transform; Barnes- G function; Variable annuity guaranteed benefits; First to default; Uncertain correlation; Unknown dependence structure; Optimal control theory.

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APA (6th Edition):

Yang, F. (2018). On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems. (Doctoral Dissertation). York University. Retrieved from http://hdl.handle.net/10315/34554

Chicago Manual of Style (16th Edition):

Yang, Fenghao. “On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems.” 2018. Doctoral Dissertation, York University. Accessed January 23, 2019. http://hdl.handle.net/10315/34554.

MLA Handbook (7th Edition):

Yang, Fenghao. “On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems.” 2018. Web. 23 Jan 2019.

Vancouver:

Yang F. On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems. [Internet] [Doctoral dissertation]. York University; 2018. [cited 2019 Jan 23]. Available from: http://hdl.handle.net/10315/34554.

Council of Science Editors:

Yang F. On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems. [Doctoral Dissertation]. York University; 2018. Available from: http://hdl.handle.net/10315/34554

2. Kim, Je Guk. Monte Carlo Methods in Finance.

Degree: 2015, University of Tennessee – Knoxville

Monte Carlo method has received significant consideration from the context of quantitative finance mainly due to its ease of implementation for complex problems in the field. Among topics of its application to finance, we address two topics: (1) optimal importance sampling for the Laplace transform of exponential Brownian functionals and (2) analysis on the convergence of quasi-regression method for pricing American option. In the first part of this dissertation, we present an asymptotically optimal importance sampling method for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals via Large deviations principle and calculus of variations the closed form solutions of which induces an optimal measure for sampling. Some numerical tests are conducted through the Dothan bond pricing model, which shows the method achieves a significant variance reduction. Secondly, we study the convergence of a quasi-regression Monte Carlo method proposed by Glasserman and Yu (2004) that is a variant of least-squares method proposed by Longstaff and Schwartz (2001) for pricing American option. Glasserman and Yu (2004) showed that the method converges to an approximation to the true price of American option with critical relations between the number of paths simulated and the number of basis functions for two examples: Brownian motion and geometric Brownian motion. We show that the method surely converges to the true price of American option even under multiple underlying assets and prove a more promising critical relation between the number of basis functions and the number of simulations in the previous study holds. Finally, we propose a rate of convergence of the method.

Subjects/Keywords: Monte Carlo; Quasi-regression; Importance sampling; Exponential Brownian functional; American option; Management Sciences and Quantitative Methods; Probability

…importance sampling of the Laplace transform of exponential Brownian functional. Convergence of the… …Monte Carlo method for estimating the Laplace transform of exponential Brownian functional of… …reduction via importance sampling for the Laplace transform of exponential Brownian functional… …transform of exponential Brownian functional. Theorem 2.8. The family of estimators {ˆ αh… …OF EXPONENTIAL BROWNIAN FUNCTIONALS 6 2.1 2.2 2.3 2.4 2.5 2.6 2.7 1 Abstract… 

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Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Kim, J. G. (2015). Monte Carlo Methods in Finance. (Doctoral Dissertation). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_graddiss/3343

Chicago Manual of Style (16th Edition):

Kim, Je Guk. “Monte Carlo Methods in Finance.” 2015. Doctoral Dissertation, University of Tennessee – Knoxville. Accessed January 23, 2019. https://trace.tennessee.edu/utk_graddiss/3343.

MLA Handbook (7th Edition):

Kim, Je Guk. “Monte Carlo Methods in Finance.” 2015. Web. 23 Jan 2019.

Vancouver:

Kim JG. Monte Carlo Methods in Finance. [Internet] [Doctoral dissertation]. University of Tennessee – Knoxville; 2015. [cited 2019 Jan 23]. Available from: https://trace.tennessee.edu/utk_graddiss/3343.

Council of Science Editors:

Kim JG. Monte Carlo Methods in Finance. [Doctoral Dissertation]. University of Tennessee – Knoxville; 2015. Available from: https://trace.tennessee.edu/utk_graddiss/3343

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