Risk Sharing with Deep Neural Networks

Paper: arXiv 2212.11752

Authors: Matteo Burzoni, Alessandro Doldi, Enea Monzio Compagnoni

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents strong theoretical rigorousness with formal convergence proofs for deep learning-based infimal convolutions in risk sharing. However, it relies primarily on numerical experiments rather than empirical market data backtests, placing it in the theoretical/deep learning domain.

Research Flowchart

  flowchart TD
    A[Research Goal: Compute Optimal Risk Sharing & Infimal Convolution via Deep Learning] --> B[Inputs: Multi-Asset Financial Positions & Agent Risk Measures]
    B --> C[Methodology: Neural Network Parameterization of Allocations & Variational Formulation]
    C --> D[Computational Process: Joint Optimization of Infimal Convolution Loss & Allocation Networks]
    D --> E[Mathematical Proofs: Convergence of Approximated Inf-Convolution & Allocations]
    E --> F[Outcomes: Validated Numerical Experiments & Scalable Multi-Asset Risk Sharing]