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Process-Based Risk Measures and Risk-Averse Control of Discrete-Time Systems

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  • Jingnan Fan
  • Andrzej Ruszczynski

Abstract

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main features are 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.

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  • Jingnan Fan & Andrzej Ruszczynski, 2014. "Process-Based Risk Measures and Risk-Averse Control of Discrete-Time Systems," Papers 1411.2675, arXiv.org, revised Nov 2016.
    • Handle: RePEc:arx:papers:1411.2675
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    References listed on IDEAS

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    Cited by:

    1. Jingnan Fan & Andrzej Ruszczyński, 2018. "Risk measurement and risk-averse control of partially observable discrete-time Markov systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 161-184, October.

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