Risk Sharing with Deep Neural Networks

TL;DR

This paper introduces a neural network framework to compute optimal risk sharing among agents with different risk measures, proving convergence and validating with numerical experiments.

Contribution

It presents a novel neural network approach for infimal convolution of risk measures and optimal allocations, with theoretical convergence guarantees.

Findings

Neural network approximations converge to theoretical risk sharing solutions.

The framework effectively computes optimal allocations in complex risk sharing scenarios.

Numerical experiments validate the accuracy and robustness of the proposed method.

Abstract

We consider the problem of optimally sharing a financial position among agents with potentially different reference risk measures. The problem is equivalent to computing the infimal convolution of the risk metrics and finding the so-called optimal allocations. We propose a neural network-based framework to solve the problem and we prove the convergence of the approximated inf-convolution, as well as the approximated optimal allocations, to the corresponding theoretical values. We support our findings with several numerical experiments.