Conditional Risk Mappings

28 Pages Posted: 4 May 2005

See all articles by Andrzej Ruszczynski

Andrzej Ruszczynski

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

Alexander Shapiro

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE)

Date Written: 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 Classification: C44, C61, D81

Suggested Citation

Ruszczynski, Andrzej and Shapiro, Alexander, Conditional Risk Mappings (April 26, 2005). Available at SSRN: https://ssrn.com/abstract=714241 or http://dx.doi.org/10.2139/ssrn.714241

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 Shapiro

Georgia Institute of Technology - The H. Milton Stewart School of Industrial & Systems Engineering (ISyE) ( email )

765 Ferst Drive
Atlanta, GA 30332-0205
United States

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