This paper studies deep learning approaches to find optimal reinsurance and dividend strategies for insurance companies. Due to the randomness of the financial ruin time to terminate the control processes, a Markov chain approximation-based iterative deep learning algorithm is developed to study this type of infinite-horizon optimal control problems. The optimal controls are approximated as deep neural networks in both cases of regular and singular types of dividend strategies. The framework of Markov chain approximation plays a key role in building the iterative equations and initialization of the algorithm. We implement our method to classic dividend and reinsurance problems and compare the learning results with existing analytical solutions. The feasibility of our method for complicated problems has been demonstrated by applying to an optimal dividend, reinsurance and investment problem under a high-dimensional diffusive model with jumps and regime switching.

中文翻译：

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最优保险策略：混合深度学习马尔可夫链逼近法

本文研究了深度学习方法，以找到保险公司的最佳再保险和分红策略。由于财务毁灭时间终止控制过程的随机性，因此开发了一种基于马尔可夫链近似的迭代深度学习算法来研究这种无限水平最优控制问题。在常规和奇异类型的分红策略中，最优控制都近似为深度神经网络。马尔可夫链近似框架在建立迭代方程和算法初始化中起着关键作用。我们将我们的方法应用于经典的股息和再保险问题，并将学习结果与现有的分析解决方案进行比较。