论文标题
半线性椭圆PDE的深神网络算法，并在保险数学中应用
A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics
论文作者
论文摘要
在计算风险措施时，在保险数学中，无限时间的最佳控制问题出现。它们的溶液对应于确定性半线性（退化）椭圆形偏微分方程的溶液。在本文中，我们提出了一种深层神经网络算法，用于在高维度中求解这种偏微分方程。该算法基于与随机终端时间的向后随机微分方程的椭圆形部分微分方程的对应关系。
In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In this paper we propose a deep neural network algorithm for solving such partial differential equations in high dimensions. The algorithm is based on the correspondence of elliptic partial differential equations to backward stochastic differential equations with random terminal time.
