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Proportional Reinsurance for Models with Stochastic Cash Reserve Rate Open Access


Other title
value function
HJB equation
The optimal policy
Type of item
Degree grantor
University of Alberta
Author or creator
Supervisor and department
Tahir, Choulli (Department of Mathematical and Statistical Sciences)
Examining committee member and department
Abel Cadenillas (Mathematical and Statistical Sciences)
Valentina Galvani (Economics)
Alexander Melnikov ( Mathematical and Statistical Sciences)
Tahir, Choulli ( Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Mathematical Finance
Date accepted
Graduation date
2017-06:Spring 2017
Master of Science
Degree level
This thesis investigates a problem of risk control for a financial corporation. Precisely, the thesis considers the case of proportional reinsurance for an insurance company. The objective is to find the optimal policy, that consists of risk control, which maximizes the total expected discounted value of cash reserve up to the bankruptcy time.The models for the cash reserve process, considered in this thesis, have stochastic drifts per unit time (that we call stochastic cash reserve rate hereafter) and constant volatility. These models extend the literature on proportional reinsurance, to the case of stochastic cash reserve rate that is either fully or partially observed. Precisely, I address three principal models. The first model deals with the case when the cash reserve rate is time dependent but deterministic. The second model assumes that the cash reserve rate process has an observable noise, while the third model assumes that the cash reserve rate is stochastic and is not observable.Thanks to the Bellman's principle, for each of these three models, I derive the Hamilton-Jacobi-Bellman equation that corresponds to the stochastic control problem. Then I solve these equations as explicitly as possible. Afterwards, I describe the optimal policy for each model in terms of the obtained optimal value function, and I state the verification theorem. Finally, I consider the case where the insurance company pays liability at a constant rate per unit time.
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.
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