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Optimal Robust Reinsurance with Multiple Insurers

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  • Emma Kroell
  • Sebastian Jaimungal
  • Silvana M. Pesenti

Abstract

We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to $n$ insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the reinsurer is uncertain about the insurers' claim severity distributions and frequencies, they design reinsurance contracts that maximise their expected wealth subject to an entropy penalty. Insurers meanwhile seek to maximise their expected utility without ambiguity. We solve this continuous-time Stackelberg game for general reinsurance contracts and find that the reinsurer prices under a distortion of the barycentre of the insurers' models. We apply our results to proportional reinsurance and excess-of-loss reinsurance contracts, and illustrate the solutions numerically. Furthermore, we solve the related problem where the reinsurer maximises, still under ambiguity, their expected utility and compare the solutions.

Suggested Citation

  • Emma Kroell & Sebastian Jaimungal & Silvana M. Pesenti, 2023. "Optimal Robust Reinsurance with Multiple Insurers," Papers 2308.11828, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2308.11828
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    References listed on IDEAS

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    1. Bo Yi & Frederi Viens & Zhongfei Li & Yan Zeng, 2015. "Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(8), pages 725-751, November.
    2. Ailing Gu & Frederi G. Viens & Yang Shen, 2020. "Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(4), pages 342-375, April.
    3. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    4. Irgens, Christian & Paulsen, Jostein, 2004. "Optimal control of risk exposure, reinsurance and investments for insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 21-51, August.
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