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Conditional Risk Mappings

Andrzej Ruszczynski (rusz***at***rutcor.rutgers.edu)
Alexander Shapiro (ashapiro***at***isye.gatech.edu)

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, Stochastic Optimization, Dynamic Programming, Multi-stage Programming.

Category 1: Stochastic Programming

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Citation: Preprint

Download: [PDF]

Entry Submitted: 02/21/2004
Entry Accepted: 02/24/2004
Entry Last Modified: 04/09/2007

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