Linear-quadratic stochastic Stackelberg differential games with asymmetric information for systems driven by multi-dimensional jump-diffusion processes

Abstract

We consider the linear-quadratic stochastic leader-follower Stackelberg differential game for jump-diffusion systems with asymmetric information. In our problem setup, given complete information $F$, leader and follower have access to partial information (filtration) $G_1\subset F$ and $G_2\subset F$, respectively, where $G_2\subset G_1$ captures asymmetric information. Our paper can be viewed as an extension of the complete information ($G_2=G_1=F$) in [15] to the problem with partial and asymmetric information. By generalizing the stochastic maximum principles and four-step schemes of [15], we obtain the state-feedback representation of the (open-loop type) Stackelberg equilibrium for the leader and the follower in terms of the coupled integro-type Riccati differential equations and the filtering (state) processes with respect to $G_2$ and $G_1$. Indeed, due to the partial and asymmetric information nature, we have to identify new types of the four-step schemes and develop different approaches to obtain the (filtering-based) state-feedback type Stackelberg equilibrium.