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Essays on proportional reinsurance under random horizon
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- Author / Creator
- Ella Elazkany
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This thesis considers proportional reinsurance that insurance companies might employ in order to reduce risks and limit the impact of large claims. An insurance company is a typical example of a financial corporation, which can choose a production policy from an available set of control policies with different expected profit and risks. In this setting, this thesis considers two main cases depending whether the company pays dividends to the shareholders or not. For both cases, the main aim lies in measuring the impact of the liability and/or the random horizon. The liability payments could reflect the mortgage on the company's property or the amortization bond, while the random horizon could model the default of a firm or the death time of an agent. When the company pays dividends, its objective consists of maximizing the expected aggregate discounted dividend distributions. However, when there is no dividend payments, the objective resides in maximizing the expected total discounted cash reserve up to the bankruptcy time or the random horizon (whoever comes first). Thanks to the Bellman's principal, the control problems in all cases are reduced to Hamilton-Jacobi-Bellman equations. Smooth solutions to these equations, which take various forms depending on the interactions between the parameters of the corporation's model and the random horizon, are explicitly derived. Furthermore, the optimal policies for each control problem are explicitly derived.
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- Graduation date
- Fall 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.