Cooperative Games with General Deviation Measures
27 Pages Posted: 6 Mar 2013
Date Written: April 2013
Cooperative games with players using different law‐invariant deviation measures as numerical representations for their attitudes towards risk in investing to a financial market are formulated and studied. As a central result, it is shown that players (investors) form a coalition (cooperative portfolio) that behaves similar to a single player (investor) with a certain deviation measure. An explicit formula for that deviation measure is obtained. An approach to optimal risk sharing among investors is developed, and a “fair” division of the cooperative portfolio expected gain, belonging to the core of a corresponding cooperative game, is suggested.
Keywords: deviation measures, cooperative games, portfolio theory, risk sharing
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