# Systemic Optimal Risk Transfer Equilibrium

## TL;DR

The paper introduces the Systemic Optimal Risk Transfer Equilibrium (SORTE), a new framework for systemic risk management that optimizes overall systemic performance by endogenously determining budget constraints, differing from classical approaches.

## Contribution

It develops the SORTE concept, establishing conditions for its existence, uniqueness, and Pareto optimality, emphasizing systemic over individual risk considerations.

## Key findings

- SORTE guarantees existence and uniqueness under broad assumptions.
- SORTE optimizes systemic performance rather than individual utility.
- The approach generalizes B"uhlmann's classical risk exchange model.

## Abstract

We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the B\"uhlmann's classical notion of an Equilibrium Risk Exchange. We provide sufficient general assumptions that guarantee existence, uniqueness, and Pareto optimality of such a SORTE. In both the B\"uhlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint. The two approaches differ by the budget constraints. In B\"uhlmann's definition the vector that assigns the budget constraint is given a priori. On the contrary, in the SORTE approach, the vector that assigns the budget constraint is endogenously determined by solving a systemic utility maximization. SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality.