Mean-variance portfolio selection under partial information by Xiong, J, Zhou, X

“…The main methodological contribution of the paper is to employ the particle system representation to develop analytical and numerical approaches in obtaining the filter as well as solving the related backward stochastic differential equation. © 2007 Society for Industrial and Applied Mathematics.…”

Existence of solutions to a class of indefinite stochastic Riccati equations by Qian, Z, Zhou, X

“…An indefinite stochastic Riccati equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. …”

Stochastic control for linear systems driven by fractional noises by Yaozhong, H, Zhou, X

“…First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are established. …”

Constrained stochastic LQ control with random coefficients, and application to portfolio selection by Hu, Y, Zhou, X

“…The ESREs, introduced for the first time in this paper, are highly nonlinear backward stochastic differential equations (BSDEs), whose solvability is proved based on a truncation function technique and Kobylanski's results. …”

A generalized Neyman-Pearson lemma for g-probabilities by Ji, S, Zhou, X

“…The problem is shown to be a special case of a general stochastic optimization problem where the objective is to choose the terminal state of certain backward stochastic differential equations so as to minimize a g-expectation. …”

Time-inconsistent stochastic linear-quadratic control: characterization and uniqueness of equilibrium by Hu, Y, Jin, H, Zhou, X

“…We derive a necessary and sufficient condition for equilibrium controls via a flow of forward–backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the explicit equilibrium control constructed in [9] is indeed unique. …”

Time-Inconsistent Stochastic Linear--Quadratic Control by Hu, Y, Jin, H, Zhou, X

“…We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we find an explicit equilibrium control. …”

Time-Inconsistent Stochastic Linear--Quadratic Control by Hu, Y, Jin, H, Zhou, X

“…We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we find an explicit equilibrium control. …”