arXiv subjects

Liangquan Zhang

Publications and source records attributed to Liangquan Zhang.

23 records · Page 2Linked to original sources

arXiv2012

Stochastic Verification Theorem of Forward-Backward Controlled Systems for Viscosity Solutions

In this paper, we investigate the controlled system described by forward-backward stochastic differential equations with the control contained in drift, diffusion and generator of BSDE. A new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions. It is worth to pointing out that this theorem has wider applicability than the restrictive classical verification theorems. As a relevant problem, the optimal stochastic feedback controls for forward-backward system are discussed as well.

math.OC↗

arXiv2011

Large Deviation for Reflected Backward Stochastic Differential Equations

In this note, we prove the Freidlin-Wentzell's large deviation principle for BSDEs with one-sided reflection.

math.PR↗

arXiv2010

Comparison Theorem of Multi-dimensional Backward Doubly Stochastic Differential Equations on Infinite Horizon

Under quasi-monotone assumptions for coefficients, we show one kind of comparison theorem for multi-dimensional\textbf{\}backward doubly stochastic differential equations on infinite horizon. An example is given as well.

math.PR↗

arXiv2010

Comparison Theorems of Infinite Horizon Forward-Backward Stochastic Differential Equations

By the methods of probability and duality technique, we give some comparison theorems for the solutions of infinite horizon forward-backwad stochastic differential equations.

math.PR↗

arXiv2010

Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications

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). And as an example of the SMP, we solve a kind of forward-backward doubly stochastic linear quadratic optimal control problems as well. In the last section, we use the solution of FBDSDEs to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and open-loop Nash equilibrium point for nonzero sum differential games problem.

math.OC↗