A General Theory of Risk Sharing
Risk Management
2026-03-04 v2 Theoretical Economics
Mathematical Finance
Abstract
We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have potentially heterogeneous risk preferences modeled by risk measures on a separable probability space. We derive the dual representation of the value function using a Strassen-type theorem for the weak-star topology and provide a characterization of the acceptance set using Aumann integration. These results are illustrated by explicit formulas when risk preferences are within the family of entropic and expected shortfall risk measures, and applications to Pareto efficiency in large markets.
Keywords
Cite
@article{arxiv.2505.19276,
title = {A General Theory of Risk Sharing},
author = {Vasily Melnikov},
journal= {arXiv preprint arXiv:2505.19276},
year = {2026}
}