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Imperfect Hedging, Efficient Hedging, Defaultable Markets, Equity Linked Life Insurance Contracts, Neyman Pearson Lemma, Regime Switching Models, Risk Minimization, Bermudan Options, Credit Risk

Nosrati, Amir

Supervisor and department: Melnikov, Alexander Mathematical and Statistical Sciences, University of Alberta

Examining committee member and department: Frei, Christoph Mathematical and Statistical Sciences, University of Alberta Hillen, Thomas Mathematical and Statistical Sciences, University of Alberta Kouritzin, Mike Mathematical and Statistical Sciences, University of Alberta Yaskin, Vladyslav Mathematical and Statistical Sciences, University of Alberta Ware, Tony Mathematics and Statistics, University of Calgary

Department: Department of Mathematical and Statistical Sciences

Specialization: Mathematical Finance

Date accepted: 2016-07-22T11:39:53Z

Graduation date: 2016-06:Fall 2016

Degree: Doctor of Philosophy

Degree level: Doctoral

Abstract: In this thesis, we study the impact of random times to model and manage unpredictable risk events in the financial models. First, as a generalization of the classical Neyman-Pearson lemma, we show how to minimize the probabil- ity of type-II-error when the null hypothesis, alternative and the significance level all are revealed to us randomly. This randomness arises some measurabil- ity requirements that we have dealt with them by using a measurable selection argument. Then, we consider a regime-switching financial model which is sub- ject to a default time satisfying the so-called the density hypothesis. For this model, we present a Girsanov type result and an explicit representation for the problem of superhedging. In both cases, the desired representation is decom- posed into an after-default and a global before-default decomposition. Another problem consists in minimizing the expected shortfall risk for defaultable se- curities under initial capital constraint. The underlying model is exposed to multiple independent default times satisfying the intensity hypothesis. We il- lustrate the results by numerical examples and the applications to Guaranteed Minimum Maturity Benefit GMMB equity-linked life insurance contracts. Finally, we construct a framework to consider a Guaranteed Minimum Death Benefit GMDB equity-linked life insurance contract as a Bermudan option. Under an initial capital constraint, we provide closed-form solutions for the quantile hedging problem of a GMDB contract with a constant guarantee.

Language: English

DOI: doi:10.7939-R3862BK6T

Rights: This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.





Author: Nosrati, Amir

Source: https://era.library.ualberta.ca/


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Imperfect Hedging in Defaultable Markets and Insurance Applications by Amir Nosrati A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematical Finance Department of Mathematical and Statistical Sciences University of Alberta c Amir Nosrati, 2016  Abstract In this thesis, we study the impact of random times to model and manage unpredictable risk events in the financial models.
First, as a generalization of the classical Neyman-Pearson lemma, we show how to minimize the probability of type-II-error when the null hypothesis, alternative and the significance level all are revealed to us randomly.
This randomness arises some measurability requirements that we have dealt with them by using a measurable selection argument.
Then, we consider a regime-switching financial model which is subject to a default time satisfying the so-called the density hypothesis.
For this model, we present a Girsanov type result and an explicit representation for the problem of superhedging.
In both cases, the desired representation is decomposed into an after-default and a global before-default decomposition.
Another problem consists in minimizing the expected shortfall risk for defaultable securities under initial capital constraint.
The underlying model is exposed to multiple independent default times satisfying the intensity hypothesis.
We illustrate the results by numerical examples and the applications to Guaranteed Minimum Maturity Benefit (GMMB) equity-linked life insurance contracts. Finally, we construct a framework to consider a Guaranteed Minimum Death Benefit (GMDB) equity-linked life insurance contract as a Bermudan option. Under an initial capital constraint, we provide closed-form solutions for the quantile hedging problem of a GMDB contract with a constant guarantee. ii Preface I, Amir Nosrati, declare that this thesis titled, “Imperfect Hedging in Defaultable Markets and Insurance Applications” and the ...





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