Optimal risk mitigation by deep reinsurance

TL;DR

This paper develops a neural network-based method to optimize reinsurance strategies for an insurance company, balancing terminal wealth and ruin probability under complex surplus dynamics.

Contribution

It introduces a novel neural network approach to solve a stochastic control problem involving reinsurance and surplus management with a complex surplus process.

Findings

Neural networks effectively optimize reinsurance strategies.

The method handles complex surplus models like Cramér-Lundberg with Ornstein-Uhlenbeck processes.

Optimal strategies improve risk mitigation and financial stability.

Abstract

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.