×

zbMATH — the first resource for mathematics

Uncertain optimal control with application to a portfolio selection model. (English) Zbl 1225.93121
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1007/s10700-010-9073-2 · Zbl 1196.34005 · doi:10.1007/s10700-010-9073-2
[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 · doi:10.1137/0327063
[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 · doi:10.1016/0022-0531(71)90038-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.