Abstract This paper studies the optimal debt ratio and dividend strategy for an insurer under the model with the coefficients depending on the state of the economy. The object is to maximize the total expected discounted utility of dividend payment of the insurer. The optimal strategy and value function are characterized by the classical solution of the associated Hamilton–Jacobi–Bellman equation which can be reduced to a system of nonlinear PDEs. Considering logarithmic and power utility, we show the existence of classical solution to the system by the ordered upper-lower solution method, and verify that the solution is indeed the value function.

中文翻译：

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制度转换模型下保险公司最优负债率与分红策略

摘要 本文研究了在系数取决于经济状况的模型下保险公司的最优负债率和分红策略。目标是使保险人支付红利的总预期贴现效用最大化。最优策略和价值函数的特征在于相关的 Hamilton-Jacobi-Bellman 方程的经典解，该方程可以简化为非线性偏微分方程系统。考虑对数效用和幂效用，我们通过有序上下解法证明了系统经典解的存在性，并验证了该解确实是价值函数。