Skip to main content
SpringerLink
Log in

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

  • Conference paper
  • First Online:
Modeling Decisions for Artificial Intelligence (MDAI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11676))

Abstract

A Markov decision process 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 risk levels for feasible ranges, firstly a risk-minimizing problem is discussed by mathematical programming. Next dynamic risk-sensitive reward maximization under risk constraints is investigated. Dynamic programming can not be applied to this dynamic optimization model, and we try other approaches. A few numerical examples are given to understand the obtained results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

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

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Bäuerle, N., Rieder, U.: More risk-sensitive Markov decision processes. Math. Oper. Res. 39, 105–120 (2014)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Yoshida, Y.: A dynamic risk allocation of value-at-risks with portfolios. J. Adv. Comput. Intell. Intell. Inform. 16, 800–806 (2012)

    Article  Google Scholar 

  9. 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 

  10. Yoshida, Y.: Coherent risk measures derived from utility functions. In: Torra, V., Narukawa, Y., Aguiló, I., González-Hidalgo, M. (eds.) MDAI 2018. LNCS (LNAI), vol. 11144, pp. 15–26. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00202-2_2

    Chapter  Google Scholar 

  11. Yoshida, Y.: Risk-sensitive decision making under risk constraints with coherent risk measures. In: Czarnowski, I. et al. (ed.) Smart Innovation, Systems and Technologies 143. Springer, Cham, June 2019, to appear

    Chapter  Google Scholar 

  12. Yoshida, Y.: Portfolio optimization in fuzzy asset management with coherent risk measures derived from risk averse utility. Neural Computing and Applications. https://doi.org/10.1007/s00521-018-3683-y

Download references

Acknowledgments

This research is supported from JSPS KAKENHI Grant Number JP 16K05282.

Author information

Authors and Affiliations

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

    Yuji Yoshida

Authors
  1. Yuji Yoshida
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuji Yoshida .

Editor information

Editors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Vicenç Torra

  2. Tamagawa University, Machida, Tokyo, Japan

    Yasuo Narukawa

  3. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  4. University of Milano-Bicocca, Milan, Italy

    Marco Viviani

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Yoshida, Y. (2019). Risk-Sensitive Markov Decision Under Risk Constraints with Coherent Risk Measures. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-26773-5_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26772-8

  • Online ISBN: 978-3-030-26773-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation