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Conditional Risk Mappings

Andrzej Ruszczynski
Rutgers, The State University of New Jersey - Rutgers Business School at Newark & New Brunswick

Alexander Shapiro
Georgia Institute of Technology - School of Industrial and Systems Engineering

April 26, 2005

Abstract:
We introduce an axiomatic definition of a conditional convex risk mapping and we derive its properties. In particular, we prove a representation theorem for conditional risk mappings in terms of conditional expectations. We also develop dynamic programming relations for multistage optimization problems involving conditional risk mappings.

Keywords: Risk, convex analysis, conjugate duality, dynamic programming

JEL Classifications: C44, C61, D81

Working Paper Series

Date posted: May 04, 2005 ; Last revised: May 04, 2005

Suggested Citation

Ruszczynski, Andrzej and Shapiro, Alexander NMI2, Conditional Risk Mappings (April 26, 2005). Available at SSRN: http://ssrn.com/abstract=714241

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Contact Information

Andrzej Ruszczynski (Contact Author) Rutgers, The State University of New Jersey - Rutgers Business School at Newark & New Brunswick ( email ) 94 Rockefeller Road Piscataway, NJ 08854 United States
Alexander NMI2 Shapiro Georgia Institute of Technology - School of Industrial and Systems Engineering ( email ) 765 Ferst Drive Atlanta, GA 30332-0205 United States