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Optimal investment problem for an insurer and a reinsurer

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Abstract

This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer: The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer’s optimal investment strategies under the two cases.

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Authors and Affiliations

  1. School of Science, Tianjin University, Tianjin, 300072, China

    Danping Li, Ximin Rong & Hui Zhao

  2. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Ximin Rong

Authors
  1. Danping Li
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  2. Ximin Rong
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  3. Hui Zhao
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Corresponding author

Correspondence to Danping Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11201335 and 11301376.

This paper was recommended for publication by Editor WANG Shouyang.

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Li, D., Rong, X. & Zhao, H. Optimal investment problem for an insurer and a reinsurer. J Syst Sci Complex 28, 1326–1343 (2015). https://doi.org/10.1007/s11424-015-3065-9

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  • DOI: https://doi.org/10.1007/s11424-015-3065-9

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