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On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems

On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems

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Title: On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems
Author: Yang, Fenghao
Abstract: 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.
Subject: Finance
Keywords: 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.
Type: Electronic Thesis or Dissertation
Rights: Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
URI: http://hdl.handle.net/10315/34554
Supervisor: Salisbury, Thomas ; Kuznetsov, Alexey
Degree: PhD - Doctor of Philosophy
Program: Mathematics & Statistics
Exam date: 2017-11-20
Publish on: 2018-05-28

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