Risk measurement and risk-averse control of partially observable discrete-time Markov systems

Jingnan Fan, Andrzej Ruszczynski

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We consider risk measurement in controlled partially observable Markov processes in discrete time. We introduce a new concept of conditional stochastic time consistency and we derive the structure of risk measures enjoying this property. We prove that they can be represented by a collection of static law invariant risk measures on the space of function of the observable part of the state. We also derive the corresponding dynamic programming equations. Finally we illustrate the results on a machine deterioration problem.

Original languageEnglish (US)
Pages (from-to)161-184
Number of pages24
JournalMathematical Methods of Operations Research
Volume88
Issue number2
DOIs
StatePublished - Oct 1 2018

Fingerprint

Risk Measures
Discrete-time
Time Consistency
Deterioration
Invariant Measure
Markov Process
Dynamic Programming
Dynamic programming
Markov processes
Risk measurement
Time consistency
Measure of risk
Markov process
Risk-averse
Risk measures
Concepts

Cite this

@article{e4c34288bdff45a9807682bc218f9258,
title = "Risk measurement and risk-averse control of partially observable discrete-time Markov systems",
abstract = "We consider risk measurement in controlled partially observable Markov processes in discrete time. We introduce a new concept of conditional stochastic time consistency and we derive the structure of risk measures enjoying this property. We prove that they can be represented by a collection of static law invariant risk measures on the space of function of the observable part of the state. We also derive the corresponding dynamic programming equations. Finally we illustrate the results on a machine deterioration problem.",
author = "Jingnan Fan and Andrzej Ruszczynski",
year = "2018",
month = "10",
day = "1",
doi = "https://doi.org/10.1007/s00186-018-0633-5",
language = "English (US)",
volume = "88",
pages = "161--184",
journal = "Mathematical Methods of Operations Research",
issn = "1432-2994",
publisher = "Physica-Verlag",
number = "2",

}

Risk measurement and risk-averse control of partially observable discrete-time Markov systems. / Fan, Jingnan; Ruszczynski, Andrzej.

In: Mathematical Methods of Operations Research, Vol. 88, No. 2, 01.10.2018, p. 161-184.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Risk measurement and risk-averse control of partially observable discrete-time Markov systems

AU - Fan, Jingnan

AU - Ruszczynski, Andrzej

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We consider risk measurement in controlled partially observable Markov processes in discrete time. We introduce a new concept of conditional stochastic time consistency and we derive the structure of risk measures enjoying this property. We prove that they can be represented by a collection of static law invariant risk measures on the space of function of the observable part of the state. We also derive the corresponding dynamic programming equations. Finally we illustrate the results on a machine deterioration problem.

AB - We consider risk measurement in controlled partially observable Markov processes in discrete time. We introduce a new concept of conditional stochastic time consistency and we derive the structure of risk measures enjoying this property. We prove that they can be represented by a collection of static law invariant risk measures on the space of function of the observable part of the state. We also derive the corresponding dynamic programming equations. Finally we illustrate the results on a machine deterioration problem.

UR - http://www.scopus.com/inward/record.url?scp=85044968287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044968287&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s00186-018-0633-5

DO - https://doi.org/10.1007/s00186-018-0633-5

M3 - Article

VL - 88

SP - 161

EP - 184

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 2

ER -