Displaying similar documents to “A general stochastic maximum principle for singular control problems.”

Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations

Jianhui Huang, Jingtao Shi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear...

A multidimensional singular stochastic control problem on a finite time horizon

Marcin Boryc, Łukasz Kruk (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.

A multidimensional singular stochastic control problem on a finite time horizon

Marcin Boryc, Łukasz Kruk (2015)

Annales UMCS, Mathematica

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A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique

On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance

Mokhtar Hafayed, Petr Veverka, Syed Abbas (2014)

Applications of Mathematics

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We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...

Partially observed optimal controls of forward-backward doubly stochastic systems

Yufeng Shi, Qingfeng Zhu (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The partially observed optimal control problem is considered for forward-backward doubly stochastic systems with controls entering into the diffusion and the observation. The maximum principle is proven for the partially observable optimal control problems. A probabilistic approach is used, and the adjoint processes are characterized as solutions of related forward-backward doubly stochastic differential equations in finite-dimensional spaces. Then, our theoretical result is applied...

On adaptive control for the continuous time-varying JLQG problem

Adam Czornik, Andrzej Świernik (2005)

International Journal of Applied Mathematics and Computer Science

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In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can...

Maximum principle for forward-backward doubly stochastic control systems and applications

Liangquan Zhang, Yufeng Shi (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short)....