On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems
dc.contributor.advisor | Salisbury, Thomas | |
dc.contributor.advisor | Kuznetsov, Alexey | |
dc.creator | Yang, Fenghao | |
dc.date.accessioned | 2018-05-28T12:57:17Z | |
dc.date.available | 2018-05-28T12:57:17Z | |
dc.date.copyright | 2017-11-20 | |
dc.date.issued | 2018-05-28 | |
dc.date.updated | 2018-05-28T12:57:17Z | |
dc.degree.discipline | Mathematics & Statistics | |
dc.degree.level | Doctoral | |
dc.degree.name | PhD - Doctor of Philosophy | |
dc.description.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. | |
dc.identifier.uri | http://hdl.handle.net/10315/34554 | |
dc.language.iso | en | |
dc.rights | Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests. | |
dc.subject | Finance | |
dc.subject.keywords | Levy processes | |
dc.subject.keywords | Kou processes | |
dc.subject.keywords | General exponential functional | |
dc.subject.keywords | Skew Brownian motion | |
dc.subject.keywords | Asymmetric local time | |
dc.subject.keywords | Mellin transform | |
dc.subject.keywords | Barnes- G function | |
dc.subject.keywords | Variable annuity guaranteed benefits | |
dc.subject.keywords | First to default | |
dc.subject.keywords | Uncertain correlation | |
dc.subject.keywords | Unknown dependence structure | |
dc.subject.keywords | Optimal control theory. | |
dc.title | On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems | |
dc.type | Electronic Thesis or Dissertation |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Yang_Fenghao_2018_PhD.pdf
- Size:
- 1.35 MB
- Format:
- Adobe Portable Document Format
- Description: