Abstract
A leader-follower stochastic differential game is considered with the state equation being a linear Ito-type stochastic differential equation and the cost functionals being quadratic. We allow that the coefficients of the system and those of the cost functionals are random, the controls enter the diffusion of the state equation, and the weight matrices for the controls in the cost functionals are not necessarily positive definite. The so-called open-loop strategies are considered only. Thus, the follower first solves a stochastic linear quadratic (LQ) optimal control problem with the aid of a stochastic Riccati equation. Then the leader turns to solve a stochastic LQ problem for a forward-backward stochastic differential equation. If such an LQ problem is solvable, one obtains an open-loop solution to the two-person leader-follower stochastic differential game. Moreover, it is shown that the open-loop solution admits a state feedback representation if a new stochastic Riccati equation is solvable.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
