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Robust reinsurance and investment strategies under principal–agent framework

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Abstract

In this paper, a class of reinsurance contracting problems is examined under a continuous-time principal–agent framework with mean-variance criteria, where a reinsurer and an insurer are assigned the roles of the principal and the agent, respectively. Both parties can manage their insurance risk by investing in a financial portfolio comprising a risk-free asset and a risky asset. It has been assumed that both the insurer and the reinsurer are concerned about model uncertainty and that they aim to find a robust reinsurance contract and robust investment strategies by maximizing their respective mean-variance cost functionals taking sets of probability scenarios into account. To articulate the time-inconsistency issue attributed to the mean-variance optimization criteria, the optimization procedure of each decision-maker has been formulated as a non-cooperative game and discussed by using an extended HJB equation, which is consistent with the extant work on time-consistent control. Moreover, explicit expressions for the robust reinsurance contract, the robust investment strategies and the value functions of the insurer and reinsurer have been obtained and presented. The numerical results and their economic interpretations are then discussed.

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Acknowledgements

The authors would like to thank the editor and the referees for insightful comments and suggestions. This paper is based on one of the chapters in a PhD thesis by the first author, and the first author acknowledges the International Cotutelle Macquarie University Research Excellence Scholarship. This work is also supported in part by the National Natural Science Foundation of China (11971172, 12071147) and the 111 Project (B14019).

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  1. Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, NSW, 2109, Australia

    Ning Wang & Tak Kuen Siu

  2. Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, Shanghai, 200062, China

    Kun Fan

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Correspondence to Kun Fan.

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Wang, N., Siu, T.K. & Fan, K. Robust reinsurance and investment strategies under principal–agent framework. Ann Oper Res 336, 981–1011 (2024). https://doi.org/10.1007/s10479-022-04696-2

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