We consider an insurance company which faces financial risk in the form of insurance claims and market-dependent surplus fluctuations. The company aims to simultaneously control its terminal wealth (e.g. at the end of an accounting period) and the ruin probability in a finite time interval by purchasing reinsurance. The target functional is given by the expected utility of terminal wealth perturbed by a modified Gerber-Shiu penalty function. We solve the problem of finding the optimal reinsurance strategy and the corresponding maximal target functional via neural networks. The procedure is illustrated by a numerical example, where the surplus process is given by a Cram\'er-Lundberg model perturbed by a mean-reverting Ornstein-Uhlenbeck process.

翻译：本文研究一家面临保险索赔和市场相关盈余波动的保险公司。该公司旨在通过购买再保险，在有限时间区间内同时控制其终端财富（例如，在会计期末）与破产概率。目标泛函由终端财富的期望效用加上修正的Gerber-Shiu惩罚函数构成。我们通过神经网络方法求解最优再保险策略及对应的最大目标泛函。通过数值算例说明该方法的应用，其中盈余过程采用经均值回归Ornstein-Uhlenbeck过程扰动的Cramér-Lundberg模型进行描述。