A second-order maximum principle for singular optimal stochastic controls

Shanjian Tang

doi:10.3934/dcdsb.2010.14.1581

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2010, Volume 14, Issue 4: 1581-1599. Doi: 10.3934/dcdsb.2010.14.1581

This issue Previous Article A Kneser-type theorem for backward doubly stochastic differential equations Next Article Stabilization of some coupled hyperbolic/parabolic equations

A second-order maximum principle for singular optimal stochastic controls

Shanjian Tang^1,

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

Received: March 2009

Revised: November 2009

Published: June 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 93E20; Secondary: 60H30, 60G35.

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