- Probab. Surveys
- Volume 2 (2005), 506-549.
On some recent aspects of stochastic control and their applications
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman’s optimality principle and Pontryagin’s maximum principle, and their modern exposition with viscosity solutions and backward stochastic differential equations. Some original proofs are presented in a unifying context including degenerate singular control problems. We emphasize key results on characterization of optimal control for diffusion processes, with a view towards applications. Some examples in finance are detailed with their explicit solutions. We also discuss numerical issues and open questions.
Probab. Surveys, Volume 2 (2005), 506-549.
First available in Project Euclid: 29 December 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 93E20, 49J20, 49L20, 60H30
Pham, Huyên. On some recent aspects of stochastic control and their applications. Probab. Surveys 2 (2005), 506--549. doi:10.1214/154957805100000195. https://projecteuclid.org/euclid.ps/1135911648