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Imperfect Hedging in Defaultable Markets and Insurance Applications Open Access


Other title
Imperfect Hedging
Efficient Hedging
Defaultable Markets
Equity Linked Life Insurance Contracts
Neyman Pearson Lemma
Regime Switching Models
Risk Minimization
Bermudan Options
Credit Risk
Type of item
Degree grantor
University of Alberta
Author or creator
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 of Mathematical and Statistical Sciences
Mathematical Finance
Date accepted
Graduation date
2016-06:Fall 2016
Doctor of Philosophy
Degree level
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.
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.
Citation for previous publication
Alexander Melnikov and Amir Nosrati, “Efficient hedging for defaultable securities and its appli- cation to equity-linked life insurance contracts”, International Journal of Theoretical and Applied Finance, Vol. 18, No. 7, 2015.

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File title: Imperfect Hedging in Defaultable Markets and Insurance Applications
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