Process-based risk measures and risk-averse control of discrete-time systems

Jingnan Fan, Andrzej Ruszczynski

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state of the base process. We apply this result to controlled Markov processes and we derive dynamic programming equations. We also derive dynamic programming equations for multistage stochastic programming with decision-dependent distributions.

Original languageEnglish (US)
JournalMathematical Programming
DOIs
StateAccepted/In press - Jan 1 2018

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Risk Measures
Discrete-time Systems
Dynamic programming
Dynamic Programming
Stochastic programming
Time Consistency
Random processes
Markov processes
Stochastic Programming
Invariant Measure
Markov Process
Stochastic Processes
Discrete-time
Dependent

Cite this

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Process-based risk measures and risk-averse control of discrete-time systems. / Fan, Jingnan; Ruszczynski, Andrzej.

In: Mathematical Programming, 01.01.2018.

Research output: Contribution to journalArticle

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