# American Institute of Mathematical Sciences

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

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.
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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