Finance and Stochastics

, Volume 7, Issue 1, pp 97–121 | Cite as

Optimal dynamic reinsurance policies for large insurance portfolios

  • Michael I. Taksar
  • Charlotte Markussen
Original Paper


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.

Key words: Stochastic control, stochastic differential equations, Black-Scholes model, controlled stochastic processes. proportional reinsurance, investments, ruin probabilities 
JEL Classification: C61, G22 
Mathematics Subject Classification (1991): 90A09, 90C40, 60H30 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michael I. Taksar
    • 1
  • Charlotte Markussen
    • 2
  1. 1.Department of Applied Mathematics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA (e-mail: US
  2. 2.Laboratory of Actuarial Mathematics, Copenhagen University, Universitetsparken 5, 2100 Copenhagen, Denmark DK

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