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

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dc.contributor.advisorSalisbury, Thomas
dc.contributor.advisorKuznetsov, Alexey
dc.creatorYang, Fenghao
dc.date.accessioned2018-05-28T12:57:17Z
dc.date.available2018-05-28T12:57:17Z
dc.date.copyright2017-11-20
dc.date.issued2018-05-28
dc.date.updated2018-05-28T12:57:17Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractA 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.
dc.identifier.urihttp://hdl.handle.net/10315/34554
dc.language.isoen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectFinance
dc.subject.keywordsLevy processes
dc.subject.keywordsKou processes
dc.subject.keywordsGeneral exponential functional
dc.subject.keywordsSkew Brownian motion
dc.subject.keywordsAsymmetric local time
dc.subject.keywordsMellin transform
dc.subject.keywordsBarnes- G function
dc.subject.keywordsVariable annuity guaranteed benefits
dc.subject.keywordsFirst to default
dc.subject.keywordsUncertain correlation
dc.subject.keywordsUnknown dependence structure
dc.subject.keywordsOptimal control theory.
dc.titleOn Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems
dc.typeElectronic Thesis or Dissertation

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