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.
This is a preview of subscription content, log in via an institution.
Bibliography
Basar T, Bernhard P (1991) H ∞ – optimal control and related minimax design problems. Birkhäuger, Boston/Cambridge
Bensoussan A (1992) Stochastic control of partially observable systems. Cambridge University Press, Cambridge
Bensoussan A, Nagai H (1997) Min–max characterization of a small noise limit on risk-sensitive control. SIAM J Control Optim 35:1093–1115
Bensoussan A, Nagai H (2000) Conditions for no breakdown and Bellman equations of risk-sensitive control. Appl Math Optim 42:91–101
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
Bensoussan A, Frehse J, Nagai H (1998) Some results on risk-sensitive control with full information. Appl Math Optim 37:1–41
Bielecki TR, Pliska SR (1999) Risk sensitive dynamic asset management. Appl Math Optim 39:337–360
Davis M, Lleo S (2008) Risk-sensitive benchmarked asset management. Quant Financ 8:415–426
Fleming WH (1995) Optimal investment models and risk-sensitive stochastic control. IMA vol Math Appl 65:75–88
Fleming WH, McEneaney WM (1995) Risk-sensitive control on an infinite horizon. SIAM J Control Optim 33:1881–1915
Fleming WH, Sheu SJ (1999) Optimal long term growth rate of expected utility of wealth. Ann Appl Probab 9(3):871–903
Fleming WH, Sheu SJ (2002) Risk-sensitive control and an optimal investment model. II. Ann Appl Probab 12(2):730–767
Hata H, Nagai H, Sheu SJ (2010) Asymptotics of the probability minimizing a “down-side” risk. Ann Appl Probab 20:52–89
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
Kelly J (1956) A new interpretation of information rate. Bell Syst Tech J 35:917–926
Kuroda K, Nagai H (2002) Risk sensitive portfolio optimization on infinite time horizon. Stoch Stoch Rep 73:309–331
Merton RC (1990) Continuous time finance. Blackwell, Malden
Nagai H (1996) Bellman equations of risk-sensitive control. SIAM J Cont Optim 34:74–101
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
Nagai H (2003) Optimal strategies for risk-sensitive portfolio optimization problems for general factor models. SIAM J Control Optim 41:1779–1800
Nagai H (2011) Asymptotics of the probability minimizing a “down-side” risk under partial information. Quant Financ 11:789–803
Nagai H (2012) Downside risk minimization via a large deviation approach. Ann Appl Probab 22:608–669
Nagai H, Peng S (2002) Risk-sensitive dynamic portfolio optimization with partial information on infinite time horizon. Ann Appl Probab 12(1):173–195
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
Pham H (2003) A large deviations approach to optimal long term investment. Financ Stoch 7:169–195
Whittle P (1981) Risk-sensitive linear/quadratic/Gaussian control. Adv Appl Probab 13:764–767
Whittle P (1990) A risk-sensitive maximum principle. Syst Control Lett 15:183–192
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this entry
Cite this entry
Nagai, H. (2014). 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_233-1
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5102-9_233-1
Received:
Accepted:
Published:
Publisher Name: Springer, London
Online ISBN: 978-1-4471-5102-9
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering
Publish with us
Chapter history
-
Latest
Risk-Sensitive Stochastic Control- Published:
- 11 September 2019
DOI: https://doi.org/10.1007/978-1-4471-5102-9_233-2
-
Original
Risk-Sensitive Stochastic Control- Published:
- 22 March 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_233-1