A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics
Mathematical Finance
2020-12-11 v2 Optimization and Control
Probability
Abstract
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.
Keywords
Cite
@article{arxiv.2010.15757,
title = {A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics},
author = {Stefan Kremsner and Alexander Steinicke and Michaela Szölgyenyi},
journal= {arXiv preprint arXiv:2010.15757},
year = {2020}
}