A stochastic maximum principle with dissipativity conditions

In this paper we prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a finite dimensional stochastic differential equation, driven by a multidimensional Wiener process. We drop the usual Lipschitz assumption on the drift term and substitute it with dissipativity conditions, allowing polynomial growth. The control enter both the drift and the diffusion term and takes values in a general metric space.

[1]  Ying Hu,et al.  Maximum principle for semilinear stochastic evolution control systems , 1990 .

[2]  Brahim Mezerdi,et al.  The maximum principle for optimal control of diffusions with non-smooth coefficients , 1996 .

[3]  Bernard Delyon,et al.  L p solutions of Backward Stochastic Dierential Equations , 2003 .

[4]  B. Øksendal,et al.  Applied Stochastic Control of Jump Diffusions , 2004, Universitext.

[5]  Bernard Delyon,et al.  Lp solutions of backward stochastic differential equations , 2003 .

[6]  S. Peng.  A general stochastic maximum principle for optimal control problems , 1990 .

[7]  Differentiability of Backward Stochastic Differential Equations in Hilbert Spaces with Monotone Generators , 2006, math/0603428.

[8]  É. Pardoux.  BSDEs, weak convergence and homogenization of semilinear PDEs , 1999 .

[9]  Shige Peng,et al.  Probabilistic interpretation for systems of quasilinear parabolic partial differential equations , 1991 .

[10]  Alain Bensoussan,et al.  Stochastic maximum principle for distributed parameter systems , 1983 .

[11]  Ying Hu,et al.  Stochastic Maximum Principle for Optimal Control of SPDEs , 2012, ArXiv.

[12]  Xunjing Li,et al.  Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps , 1994 .

[13]  I. Karatzas,et al.  The Stochastic Maximum Principle for Linear, Convex Optimal Control with Random Coefficients , 1995 .

[14]  Zhou Yu.  A unified treatment of maximum principle and dynamic programming in stochastic controls , 1991 .

[15]  Qi Lu,et al.  General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions , 2012, 1204.3275.

[16]  Qingxin Meng,et al.  A Maximum Principle for Optimal Control of Stochastic Evolution Equations , 2013, SIAM J. Control. Optim..

[17]  X. Zhou,et al.  Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .