Global solutions of stochastic Stackelberg differential games under convex control constraint (Q2242947)

A Stackelberg stochastic differential game on a finite horizon is considered under two alternative information constraints: controls adapted to the natural filtration of the driving Brownian motion, or controls that in addition can use the current state. Under the hypothesis that the follower has a unique response to the leader's policy, the resulting stochastic control problem for the leader is analyzed using fully coupled forward backward stochastic differential equations for the original plus the adjoint variables, in order to derive necessary conditions for optimality. The special case of linear quadratic problems is worked out in detail.