Risk sharing for capital requirements with multidimensional security markets

TL;DR

This paper investigates how heterogeneous agents with different capital adequacy tests and security market access can share risk optimally, establishing conditions for representative agents and analyzing specific frameworks for robustness.

Contribution

It introduces new conditions for the existence of representative agents and optimal risk allocations in multidimensional security markets with heterogeneous agents.

Findings

Existence of optimal risk allocations proven for polyhedral and distribution-based constraints.

Conditions for the existence of a representative agent are identified.

Robustness of the risk sharing frameworks is analyzed.

Abstract

We consider the risk sharing problem for capital requirements induced by capital adequacy tests and security markets. The agents involved in the sharing procedure may be heterogeneous in that they apply varying capital adequacy tests and have access to different security markets. We discuss conditions under which there exists a representative agent. Thereafter, we study two frameworks of capital adequacy more closely, polyhedral constraints and distribution based constraints. We prove existence of optimal risk allocations and equilibria within these frameworks and elaborate on their robustness.