Stable Allocations of Risk
20 Pages Posted: 28 May 2011
Date Written: October 5, 2007
The measurement and the allocation of risk are fundamental problems of portfolio management. Coherent measures of risk provide an axiomatic approach to the former problem. In an environment given by a coherent measure of risk and the various portfolios’ realization vectors, risk allocation games aim at solving the second problem: How to distribute the diversification benefits of the various portfolios? Understanding these cooperative games helps us to find stable, efficient, and fair allocations of risk.
We show that the class of risk allocation and totally balanced games coincide hence a stable allocation of risk is always possible. When the aggregate portfolio is riskless: risk is limited to subportfolios, the class of risk allocation games coincides with the class of exact games. As in exact games any subcoalition may be subject to marginalization even in core allocations, our result further emphasizes the responsibility in allocating risk.
Keywords: Coherent Measures of Risk, Risk Allocation Games, Totally Balanced Games, Exact Games
JEL Classification: C71, G10
Suggested Citation: Suggested Citation