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Quantile Hedging for Defaultable Securities
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- Author / Creator
- Horak, Bohdan
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This thesis investigates the hedging of equity-linked life insurance contracts with default time. In such a case the market is no longer complete and as such we consider imperfect hedging technique called Quantile Hedging. This hedging technique maximizes the probability of a successful hedge while allowing for a possibility of shortfall. This allows for a smaller amount of initial capital to be required for hedging. First, we present a multi-dimensional market with default and then extending on previous results derive a general formula in the framework of a defaultable Black-Scholes model. We then formulate the hedging problem as a Neyman-Pearson problem with composite hypothesis against a simple alternative. We apply a convex duality approach to derive a solution to the quantile hedging problem of general derivative contract within a Black Scholes market with default.We then introduce mortality of the client to the model, and using previously derived results provide closed form solutions to this problem in the case of one and two risky assets for an option to exchange one asset for another. We use these formulas to provide illustrative examples for both one and two risky asset cases and examine the relationships between shortfall probability, initial capital available for hedging, survival probability and default probability.
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- Subjects / Keywords
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- Graduation date
- Spring 2019
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.