Includes bibliographical references. / In this dissertation we set to find the dual optimal policy of a dividend payout scheme for shareholders with a risk-averse utility function and the retention level of received premiums for an insurance company with the option of reinsurance. We set the problem as a stochastic control problem. We then solve the resulting second-order partial differential equation known as Hamilton-Jacobi-Bellman equation. We find out that the optimal retention level is linear with the current reserve up to a point whereupon it is optimal for the insurance company to retain all business. As for the optimal dividend payout scheme, we find out that it is optimal for the company not to declare dividends and we make further explorations of this result.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/13223 |
| Date | January 2014 |
| Creators | Marufu, Humphery |
| Contributors | Mataramvura, Sure |
| Publisher | University of Cape Town, Faculty of Commerce, Division of Actuarial Science |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Master Thesis, Masters, MPhil |
| Format | application/pdf |
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