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Time-inconsistent multistage stochastic programs: martingale bounds

Alois Pichler (alois.pichler***at***univie.ac.at)
Georg Ch Pflug (georg.pflug***at***univie.ac.at)

Abstract: Abstract. It is well known that multistage programs, which maximize expectation or expected utility, allow a dynamic programming formulation, and that other objectives destroy the dynamic programming character of the problem. This paper considers a risk measure at the final stage of a multistage stochastic program. Although these problems are not time consistent, it is shown that optimal decisions evolve as a martingale. A verification theorem is provided, which characterizes optimal decisions by enveloping sub- and supermartingales. To obtain these characterizations the idea of a constant risk profile has to be given up and instead a risk profile, which varies over time, has to be accepted. The basis of the analysis is a new decomposition theorem for risk measures, which is able to recover the genuine risk measure by measuring risk conditionally.

Keywords: Stochastic Optimization, Average Value-at-Risk, dynamic Programming

Category 1: Stochastic Programming

Category 2: Other Topics (Dynamic Programming )

Citation: University of Vienna

Download: [PDF]

Entry Submitted: 11/24/2011
Entry Accepted: 11/24/2011
Entry Last Modified: 08/18/2014

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