A second-order maximum principle for singular optimal stochastic controls

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November 2010, 14(4): 1581-1599. doi: 10.3934/dcdsb.2010.14.1581

A second-order maximum principle for singular optimal stochastic controls

1.	Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received March 2009 Revised November 2009 Published August 2010

Abstract
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A singular optimal stochastic control problem is studied. A second-order maximum principle is presented. The second-order adjoint processes are involved, though the diffusion of the control system is control independent. The range theorem of vector-valued measures is used to prove the maximum principle. Examples are given to illustrate the applications.

Keywords: first and second adjoint processes, vector-valued measure theory., second-order maximum principle, Singular optimal stochastic control, spike variation.

Mathematics Subject Classification: Primary: 93E20; Secondary: 60H30, 60G3.

Citation: Shanjian Tang. A second-order maximum principle for singular optimal stochastic controls. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1581-1599. doi: 10.3934/dcdsb.2010.14.1581

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