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Risk-Sensitive Stochastic Control

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Encyclopedia of Systems and Control
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Abstract

Motivated by understanding “robustness” from the view points 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.

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Bibliography

  • Basar T, Bernhard P (1991) H – optimal control and related minimax design problems. Birkhäuger, Boston/Cambridge

    Google Scholar 

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

    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

    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

    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

    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

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Google Scholar 

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

    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

    MathSciNet  Google Scholar 

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

    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

    MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  Google Scholar 

  • Merton RC (1990) Continuous time finance. Blackwell, Malden

    Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    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

    MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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Nagai, H. (2015). Risk-Sensitive Stochastic Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_233

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