Open Access
2005 On some recent aspects of stochastic control and their applications
Huyên Pham
Probab. Surveys 2: 506-549 (2005). DOI: 10.1214/154957805100000195


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.


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Huyên Pham. "On some recent aspects of stochastic control and their applications." Probab. Surveys 2 506 - 549, 2005.


Published: 2005
First available in Project Euclid: 29 December 2005

zbMATH: 1189.93146
MathSciNet: MR2203679
Digital Object Identifier: 10.1214/154957805100000195

Primary: 93E20, 49J20, 49L20, 60H30

Keywords: Backward stochastic differential equations , controlled diffusions , dynamic programming , finance , maximum principle , viscosity solutions

Rights: Copyright © 2005 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.2 • 2005
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