Stable allocations of risk

• Published in: Games and economic behavior Vol. 67; no. 1; pp. 266 - 276
• Main Authors: Csóka, Péter, Herings, P. Jean-Jacques, Kóczy, László Á.
• Format: Journal Article
• Language: English
• Published: Duluth Elsevier Inc 01.09.2009; Elsevier; Academic Press
• Series: Games and Economic Behavior
• Subjects: Allocations; Coherent measures of risk; Coherent measures of risk Risk allocation games Totally balanced games Exact games; Cooperation; Diversification; Exact games; Game theory; Measurement; Portfolio management; Responsibility; Risk; Risk allocation games; Studies; Totally balanced games; Totally balanced games; Exact games; C71; Coherent measures of risk; G10; Risk allocation games
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2008.11.001

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, 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 involved in allocating risk.