Cooperative Games with General Deviation Measures

27 Pages Posted: 6 Mar 2013

See all articles by Bogdan Grechuk

Bogdan Grechuk

affiliation not provided to SSRN

Anton Molyboha

affiliation not provided to SSRN

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences

Date Written: April 2013

Abstract

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

Suggested Citation

Grechuk, Bogdan and Molyboha, Anton and Zabarankin, Michael, Cooperative Games with General Deviation Measures (April 2013). Mathematical Finance, Vol. 23, Issue 2, pp. 339-365, 2013, Available at SSRN: https://ssrn.com/abstract=2229087 or http://dx.doi.org/10.1111/j.1467-9965.2011.00495.x

Bogdan Grechuk

affiliation not provided to SSRN

No Address Available

Anton Molyboha

affiliation not provided to SSRN

No Address Available

Michael Zabarankin (Contact Author)

Stevens Institute of Technology - Department of Mathematical Sciences ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://personal.stevens.edu/~mzabaran/

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