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Optimal reinsurance strategy under fixed cost and delay

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  • Egami, Masahiko
  • Young, Virginia R.

Abstract

We consider an optimal reinsurance strategy in which the insurance company (1) monitors the dynamics of its surplus process, (2) optimally chooses a time to begin negotiating with a reinsurer to buy quota-share, or proportional, reinsurance, which introduces an implementation delay (denoted by ), (3) chooses the optimal proportion at the beginning of the negotiation period, and (4) pays a fixed transaction cost when the contract is signed ( units of time after negotiation begins). This setup leads to a combined problem of optimal stopping and stochastic control. We obtain a solution for the value function and the corresponding optimal strategy, while demonstrating the solution procedure in detail. It turns out that the optimal continuation region is a union of two intervals, a rather rare occurrence in optimal stopping. Numerical examples are given to illustrate our results and we discuss relevant economic insights from this model.

Suggested Citation

  • Egami, Masahiko & Young, Virginia R., 2009. "Optimal reinsurance strategy under fixed cost and delay," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 1015-1034, March.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:3:p:1015-1034
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    Cited by:

    1. Li, Peng & Zhou, Ming & Yao, Dingjun, 2022. "Optimal time for the excess of loss reinsurance with fixed costs," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 466-475.
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    3. Qiang Zhang & Ping Chen, 2020. "Optimal Reinsurance and Investment Strategy for an Insurer in a Model with Delay and Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 777-801, June.
    4. Matteo Brachetta & Claudia Ceci, 2021. "Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences," Mathematics, MDPI, vol. 9(4), pages 1-20, February.
    5. Matteo Brachetta & Claudia Ceci, 2021. "Optimal reinsurance problem under fixed cost and exponential preferences," Papers 2101.04975, arXiv.org.

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