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<p>We study a stochastic differential game in an insurance context. In our setting two insurers compete for market share, which is represented by a joint performance functional. Consequently, one of the insurers strives to maximize it, while the other seeks to minimize it. As a modeling basis we use classical surplus processes extended by dynamic reinsurance opportunities, which allows us to use techniques from the theory of piecewise deterministic Markov processes to analyze the resulting game. In this context, we show that a dynamic programming principle for the upper and lower value of the game holds true and that these values are unique viscosity solutions to the associated Bellman-Isaacs equations. Finally, we provide some numerical illustrations.</p>

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Optimal reinsurance in a competitive market

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月1日

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  • Lea Enzi,
  • Stefan Thonhauser

摘要

We study a stochastic differential game in an insurance context. In our setting two insurers compete for market share, which is represented by a joint performance functional. Consequently, one of the insurers strives to maximize it, while the other seeks to minimize it. As a modeling basis we use classical surplus processes extended by dynamic reinsurance opportunities, which allows us to use techniques from the theory of piecewise deterministic Markov processes to analyze the resulting game. In this context, we show that a dynamic programming principle for the upper and lower value of the game holds true and that these values are unique viscosity solutions to the associated Bellman-Isaacs equations. Finally, we provide some numerical illustrations.