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Risk-Sensitive Decision-Making Under Risk Constraints with Coherent Risk Measures

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Intelligent Decision Technologies 2019

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 143))

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Abstract

Risk-sensitive decision-making with constraints of coherent risk measures is discussed. 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. To find feasible regions, first, 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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References

  1. Acerbi, C.: Spectral measures of risk: a coherent representation of subjective risk aversion. J. Bank. Financ. 26, 1505–1518 (2002)

    Article  Google Scholar 

  2. Adam, A., Houkari, M., Laurent, J.-P.: Spectral risk measures and portfolio selection. J. Bank. Financ. 32, 1870–1882 (2008)

    Article  Google Scholar 

  3. Arrow, K.J.: Essays in the Theory of Risk-Bearing. Markham, Chicago (1971)

    MATH  Google Scholar 

  4. Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Coherent measures of risk. Math. Financ. 9, 203–228 (1999)

    Article  MathSciNet  Google Scholar 

  5. Defourny, B., Ernst, D., Wehenkel, L.: Risk-aware decision making and dynamic programming. In: Proceedings of NIPS-08 Workshop on Model Uncertainty and Risk in Reinforcement Learning, pp. 1–8 (2008)

    Google Scholar 

  6. Delage, E., Mannor, S.: Percentile optimization for MDP with parameter uncertainty. Oper. Res. 58, 203–213 (2010)

    Article  MathSciNet  Google Scholar 

  7. Howard, R., Matheson, J.: Risk-sensitive Markov decision processes. Manag. Sci. 18, 356–369 (1972)

    Article  MathSciNet  Google Scholar 

  8. Jorion, P.: Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill, New York (2006)

    Google Scholar 

  9. Kusuoka, S.: On law-invariant coherent risk measures. Adv. Math. Econ. 3, 83–95 (2001)

    Article  MathSciNet  Google Scholar 

  10. Mannor, S., Tsitsiklis, J.: Mean-variance optimization in Markov decision processes. In: Proceedings of the 28th International Conference on Machine Learning, pp. 1–22 (2011)

    Google Scholar 

  11. Ohtsubo, Y.: Optimal threshold probability in undiscounted Markov decision processes with a target set. Appl. Math. Comput. 149, 519–532 (2004)

    MathSciNet  MATH  Google Scholar 

  12. Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. J. Risk 2, 21–41 (2000)

    Article  Google Scholar 

  13. Sarykalin, S., Serraino, G., Uryasev, S.: Value-at-risk vs. conditional value-at-risk in risk management and optimization. In: Tutorials in Informs Research, pp. 270–294 (2008). https://doi.org/10.1287/educ.1080.0052

    Chapter  Google Scholar 

  14. Tasche, D.: Expected shortfall and beyond. J. Bank. Financ. 26, 1519–1533 (2002)

    Article  Google Scholar 

  15. Yoshida, Y.: Maximization of returns under an average value-at-risk constraint in fuzzy asset management. Procedia Comput. Sci. 112, 11–20 (2017)

    Article  Google Scholar 

  16. Yoshida, Y.: Coherent risk measures derived from utility functions. Modeling Decisions for Artificial Intelligence—MDAI 2018, LNAI vol. 11144, pp. 15–26. Springer, Berlin (2018)

    Chapter  Google Scholar 

  17. Yoshida, Y.: Portfolio optimization in fuzzy asset management with coherent risk measures derived from risk averse utility. Neural Comput. Appl. (2018). https://doi.org/10.1007/s00521-018-3683-y

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Authors and Affiliations

  1. University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu, 802-8577, Japan

    Yuji Yoshida

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  1. Yuji Yoshida
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Correspondence to Yuji Yoshida .

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Editors and Affiliations

  1. Department of Information Systems, Gdynia Maritime University, Gdynia, Poland

    Ireneusz Czarnowski

  2. Bournemouth University and KES International, Poole, Dorset, UK

    Robert J. Howlett

  3. University of Canberra, Canberra, ACT, Australia

    Lakhmi C. Jain

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Yoshida, Y. (2019). Risk-Sensitive Decision-Making Under Risk Constraints with Coherent Risk Measures. In: Czarnowski, I., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies 2019. Smart Innovation, Systems and Technologies, vol 143. Springer, Singapore. https://doi.org/10.1007/978-981-13-8303-8_19

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