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Imperfect Hedging in Defaultable Markets and Insurance Applications

  • Author / Creator
    Nosrati, Amir
  • 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.

  • Subjects / Keywords
  • Graduation date
    2016-06:Fall 2016
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3862BK6T
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematical Finance
  • Supervisor / co-supervisor and their department(s)
    • Melnikov, Alexander (Mathematical and Statistical Sciences, University of Alberta)
  • Examining committee members and their departments
    • Kouritzin, Mike (Mathematical and Statistical Sciences, University of Alberta)
    • Hillen, Thomas (Mathematical and Statistical Sciences, University of Alberta)
    • Yaskin, Vladyslav (Mathematical and Statistical Sciences, University of Alberta)
    • Frei, Christoph (Mathematical and Statistical Sciences, University of Alberta)
    • Ware, Tony (Mathematics and Statistics, University of Calgary)