Optimal dynamic reinsurance policies for large insurance portfolios

Charlotte Markussen and Michael I. Taksar ()
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Charlotte Markussen: Laboratory of Actuarial Mathematics, Copenhagen University, Universitetsparken 5, 2100 Copenhagen, Denmark Manuscript
Michael I. Taksar: Department of Applied Mathematics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA

Finance and Stochastics, 2003, vol. 7, issue 1, 97-121

Abstract: We consider a large insurance company whose surplus (reserve) is modeled by a Brownian motion. The company invests its surplus in stock market assets which may or may not contain an element of risk. To minimize the insurance risk there is a possibility to reinsure a part or the whole insurance portfolio. We consider the case of proportional reinsurance. There is a transaction cost, which manifests itself in the fact that the safety loading of the reinsurer is larger than that of the cedent. Stochastic optimal control theory is used to determine the optimal reinsurance policy which minimizes the ruin probability of the cedent.

Keywords: Stochastic control; stochastic differential equations; Black-Scholes model; controlled stochastic processes. proportional reinsurance; investments; ruin probabilities (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2002-11-13
Note: received: February 2001; final version received: February 2002
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