Advances and Applications in Statistics
Volume 9, Issue 1, Pages 71 - 100
(June 2008)
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OPTIMAL MANAGEMENT OF THE SAFETY LOADING AND THE EXPOSURE TO PROPORTIONAL REINSURANCE COVERAGE OF AN ORDINARY INSURANCE SYSTEM USING A DIFFUSION APPROXIMATION
Alexandros A. Zimbidis (Greece)
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Abstract: In this paper, we consider the problem of the optimal premium management of a typical insurance system using two alternative approaches: the first with no reinsurance and the second with a reinsurance option. We employ a modified version of the standard solvency equation in which the premium and the proportion of reinsurance coverage is not fixed but smoothly controlled over the whole time period. Then, we apply a diffusion approximation and using the Hamilton-Jacobi-Bellman equation, we derive the optimal strategy for the level of premium and reinsurance coverage by minimizing the potential fluctuation of premium rates and the deviations of the reserve fund from the initial value. The final results provide some useful but not trivial insight into the basic problem. |
Keywords and phrases: risk process, diffusion approximation, stochastic optimal control, HJB equation. |
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