Skip to main content
SpringerLink
Log in

Risk-Sensitive Stochastic Control

  • Living reference work entry
  • Latest version View entry history
  • First Online:
Encyclopedia of Systems and Control

  • 65 Accesses

Abstract

Motivated by understanding “robustness” from the viewpoints of stochastic control, the studies of risk-sensitive control have been developed. The idea was applied to portfolio optimization problems in mathematical finance, from which new kinds of problem on stochastic control, named “large deviation control,” have been brought and currently the studies are in progress.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Bibliography

  • Basar T, Bernhard P (1991) H∞ – optimal control and related minimax design problems. Birkhäuser, Basel

    Book  Google Scholar 

  • Bensoussan A (1992) Stochastic control of partially observable systems. Cambridge University Press, Cambridge/New York

    Book  Google Scholar 

  • Bensoussan A, Nagai H (1997) Min – max characterization of a small noise limit on risk-sensitive control. SIAM J Control Optim 35:1093–1115

    Article  MathSciNet  Google Scholar 

  • Bensoussan A, Nagai H (2000) Conditions for no breakdown and Bellman equations of risk-sensitive control. Appl Math Optim 42:91–101

    Article  MathSciNet  Google Scholar 

  • Bensoussan A, Van Schuppen JH (1985) Optimal control of partially observable stochastic systems with an exponential-of-integral performance index. SIAM J Control Optim 23:599–613

    Article  MathSciNet  Google Scholar 

  • Bensoussan A, Frehse J, Nagai H (1998) Some results on risk-sensitive control with full information. Appl Math Optim 37:1–41

    Article  MathSciNet  Google Scholar 

  • Bielecki TR, Pliska SR (1999) Risk sensitive dynamic asset management. Appl Math Optim 39:337–360

    Article  MathSciNet  Google Scholar 

  • Davis M, Lleo S (2008) Risk-sensitive benchmarked asset management. Quant Finan 8:415–426

    Article  MathSciNet  Google Scholar 

  • Davis M, Lleo S (2015) Risk-sensitive investment management. World Scientific, Singapore

    MATH  Google Scholar 

  • Elliott RJ, Kalton NJ (1972) The existence of value in differential games. Memoirs Am Math Soc (126)

    Google Scholar 

  • Fleming WH (1995) Optimal investment models and risk-sensitive stochastic control. IMA Math Appl 65:75–88

    MATH  Google Scholar 

  • Fleming WH, McEneaney WM (1995) Risk-sensitive control on an infinite horizon. SIAM J Control Optim 33:1881–1915

    Article  MathSciNet  Google Scholar 

  • Fleming WH, Sheu SJ (1999) Optimal long term growth rate of expected utility of wealth. Ann Appl Probab 9(3):871–903

    Article  MathSciNet  Google Scholar 

  • Fleming WH, Sheu SJ (2002) Risk-sensitive control and an optimal investment model. II Ann Appl Probab 12(2):730–767

    Article  MathSciNet  Google Scholar 

  • Hata H, Nagai H, Sheu SJ (2010) Asymptotics of the probability minimizing a “down-side ”risk. Ann Appl Probab 20:52–89

    Article  MathSciNet  Google Scholar 

  • Jacobson DH (1973) Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games. IEEE Trans Auto Control 18:124–131

    Article  MathSciNet  Google Scholar 

  • Karatzas I, Shreve SE (2010) Methods of mathematical finance. Springer, New York

    MATH  Google Scholar 

  • Kelly J (1956) A new interpretation of information rate. Bell Syst Tech J 35:917–926

    Article  MathSciNet  Google Scholar 

  • Kuroda K, Nagai H (2002) Risk sensitive portfolio optimization on infinite time horizon. Stochastics Stochastics Rep 73:309–331

    Article  MathSciNet  Google Scholar 

  • Merton RC (1998) Continuous time finance. Blackwell, Malden

    MATH  Google Scholar 

  • Nagai H (1996) Bellman equations of risk-sensitive control. SIAM J Control Optim 34:74–101

    Article  MathSciNet  Google Scholar 

  • Nagai H (1999) Risk-sensitive dynamic asset management with partial information. Stochastics in finite and infinite dimensions, a volume in honor of G. Kallianpur. Birkhäuser, Boston, pp 321–340

    Chapter  Google Scholar 

  • Nagai H (2003) Optimal strategies for risk-sensitive portfolio optimization problems for general factor models. SIAM J Control Optim 41:1779–1800

    Article  MathSciNet  Google Scholar 

  • Nagai H (2011) Asymptotics of the probability minimizing a “down-side” risk under partial information. Quant Finan 11:789–803

    Article  Google Scholar 

  • Nagai H (2012) Downside risk minimization via a large deviation approach. Ann Appl Probab 22:608–669

    Article  MathSciNet  Google Scholar 

  • Nagai H, Peng S (2002) Risk-sensitive dynamic portfolio optimization with partial information on infinite time horizon. Ann Appl Probab 12(1):173–195

    Article  MathSciNet  Google Scholar 

  • Nagai H, Runggaldier WJ (2008) PDE approach to utility maximization for market models with hidden Markov factors. In: Dalang RC et al (eds) Seminar on stochastic analysis, random fields and applications V, Progress in probability. Birkhäser, Basel, pp 493–506

    Chapter  Google Scholar 

  • Pham H (2003) A large deviations approach to optimal long term investment. Finance Stochast 7:169–195

    Article  MathSciNet  Google Scholar 

  • Whittle P (1981) Risk-sensitive linear/quadratic/Gaussian control. Adv Appl Probab 13:764–767

    Article  MathSciNet  Google Scholar 

  • Whittle P (1990) A risk-sensitive maximum principle. Syst Control Lett 15:183–192

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kansai University, Osaka, Japan

    Hideo Nagai

Authors
  1. Hideo Nagai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), Beijing, China

    Lei Guo

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag London Ltd., part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Nagai, H. (2019). Risk-Sensitive Stochastic Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_233-2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_233-2

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Risk-Sensitive Stochastic Control
    Published:
    11 September 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_233-2

  2. Original

    Risk-Sensitive Stochastic Control
    Published:
    22 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_233-1

Search

Navigation