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Risk-sensitive Markov Decision Processes with Risk Constraints of Coherent Risk Measures in Fuzzy and Stochastic Environment

Topics: Fuzzy Decision Analysis, Multi-Criteria Decision Making and Decision Support; Fuzzy Methods in Knowledge Discovery, Machine Learning, Approximate Reasoning, Information Fusion; Industrial, Financial, Medical, and Other Applications Using Fuzzy Methods

Author: Yuji Yoshida

Affiliation: Faculty of Economics and Business Administration, The University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577 and Japan

Keyword(s): Rrisk-sensitive Reward, Risk Constraint, Coherent Risk Measure, Weighted Average Value-at-Risk, Risk Averse Utility, Fuzzy Random Variable, Perception-based Extension.

Abstract: Risk-sensitive decision making with constraints of coherent risk measures is discussed in Markov decision processes. Risk-sensitive expected rewards under utility functions are approximated by weighted average value-at-risks, and risk constraints are described by coherent risk measures. In this paper, coherent risk measures are represented as weighted average value-at-risks with the best risk spectrum derived from decision maker’s risk averse utility, and the risk spectrum can inherit the risk averse property of the decision maker’s utility as weighting. By perception-based extension for fuzzy random variables, a dynamic portfolio model with coherent risk measures is introduced. To find feasible regions, firstly a dynamic risk-minimizing problem is discussed by mathematical programming. Next a risk-sensitive reward maximization problem under the feasible coherent risk constraints is demonstrated. A few numerical examples are given to understand the obtained results.

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Paper citation in several formats:
Yoshida, Y. (2019). Risk-sensitive Markov Decision Processes with Risk Constraints of Coherent Risk Measures in Fuzzy and Stochastic Environment. In Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019) - FCTA; ISBN 978-989-758-384-1; ISSN 2184-3236, SciTePress, pages 269-277. DOI: 10.5220/0007957502690277

@conference{fcta19,
author={Yuji Yoshida},
title={Risk-sensitive Markov Decision Processes with Risk Constraints of Coherent Risk Measures in Fuzzy and Stochastic Environment},
booktitle={Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019) - FCTA},
year={2019},
pages={269-277},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007957502690277},
isbn={978-989-758-384-1},
issn={2184-3236},
}

TY - CONF

JO - Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019) - FCTA
TI - Risk-sensitive Markov Decision Processes with Risk Constraints of Coherent Risk Measures in Fuzzy and Stochastic Environment
SN - 978-989-758-384-1
IS - 2184-3236
AU - Yoshida, Y.
PY - 2019
SP - 269
EP - 277
DO - 10.5220/0007957502690277
PB - SciTePress

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