arXiv subjects

Guangchen Wang

Publications and source records attributed to Guangchen Wang.

22 records · Page 2Linked to original sources

arXiv2018

Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information

This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term "overlapping" means that there are common part between the follower's and the leader's information, while they have no inclusion relation. Optimal controls of the follower and the leader are obtained by the stochastic maximum principle, the direct calculation of the derivative of the cost functional and stochastic filtering. A new system of Riccati equations is introduced to represent the state estimate feedback of the Stackelberg equilibrium strategy. A special solvable case is then studied and is applied to the continuous-time principal-agent problem.

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arXiv2017

A kind of linear quadratic non-zero sum differential game of backward stochastic differential equation with asymmetric information

This paper focuses on a kind of linear quadratic non-zero sum differential game driven by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu [IEEE TAC (2010) 55: 1742-1747, Automatica (2012) 48: 342-352]. Different from Wang and Yu [IEEE TAC (2010) 55: 1742-1747, Automatica (2012) 48: 342-352], novel motivations for studying this kind of game are provided. Some feedback Nash equilibrium points are uniquely obtained by forward-backward stochastic differential equations, their filters and the corresponding Riccati equations with Markovian setting.

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arXiv2017

An optimal control problem for mean-field forward-backward stochastic differential equation with noisy observation

This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are linear with respect to the state and its expectation. The control problem is different from the existing literature on optimal control for mean-field stochastic systems, and has more applications in mathematical finance, e.g., asset-liability management problem with recursive utility, systematic risk model. Using a backward separation method with a decomposition technique, two optimality conditions along with two coupled forward-backward optimal filters are derived. Several linear-quadratic optimal control problems for mean-field forward-backward stochastic differential equations are studied. Closed-form optimal solutions are explicitly obtained in detailed situations.

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arXiv2015

Leader-Follower Stochastic Differential Game with Asymmetric Information and Applications

This paper is concerned with a leader-follower stochastic differential game with asymmetric information, where the information available to the follower is based on some sub-$σ$-algebra of that available to the leader. Such kind of game problem has wide applications in finance, economics and management engineering such as newsvendor problems, cooperative advertising and pricing problems. Stochastic maximum principles and verification theorems with partial information are obtained, to represent the Stackelberg equilibrium. As applications, a linear-quadratic leader-follower stochastic differential game with asymmetric information is studied. It is shown that the open-loop Stackelberg equilibrium admits a state feedback representation if some system of Riccati equations is solvable.

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