Uncertain optimal control with application to a portfolio selection model. (English) Zbl 1225.93121

Zhu, Yuanguo

Cybern. Syst. 41, No. 7, 535-547 (2010).

Summary: Optimal control is a very important field of study not only in theory but in applications, and stochastic optimal control is also a significant branch of research in theory and applications. Based on the concept of uncertain processes, an uncertain optimal control problem is dealt with. Applying Bellman’s principle of optimality, a principle of optimality for an uncertain optimal control is obtained, and then a fundamental result called the equation of optimality in uncertain optimal control is given. Finally, as an application, the equation of optimality is used to solve a portfolio selection model.

MSC:

93E20	Optimal stochastic control
49L20	Dynamic programming in optimal control and differential games

Keywords:

equation of optimality; optimal control; portfolio selection; principle of optimality; uncertain process

References:

[1]	DOI: 10.1007/s10700-010-9073-2 · Zbl 1196.34005
[2]	Dixit A. K., Investment under uncertainty (1994)
[3]	Fleming W. H., Deterministic and stochastic optimal control (1986)
[4]	Harrison J. M., Brownian motion and stochastic flow systems (1985) · Zbl 0659.60112
[5]	Kao E. P. C., An introduction to stochastic processes (1997)
[6]	DOI: 10.1137/0327063 · Zbl 0701.90008
[7]	Liu B., Uncertainty theory,, 2. ed. (2007) · Zbl 1141.28001
[8]	Liu B., Journal of Uncertain Systems 2 pp 3– (2008)
[9]	Liu B., Journal of Uncertain Systems 3 pp 3– (2009)
[10]	Liu B., Theory and practice of uncertain programming,, 2. ed. (2009) · Zbl 1158.90010
[11]	Liu B., Uncertainty theory: A branch of mathematics for modeling human uncertainty (2010)
[12]	DOI: 10.1016/0022-0531(71)90038-X · Zbl 1011.91502