Pareto optimality in finite horizon LQ stochastic differential games

This paper is concerned with the linear quadratic (LQ) Pareto optimal control of the continuous-time stochastic systems in finite horizon. First, based on the necessary and sufficient characterization of the Pareto optimality, we reformulate the Pareto optimality problem as a set of finite horizon optimal control problems with a specific constraint structure. Next, in the spirit of the Lagrange multiplier theorem, we present a necessary condition for a control to be Pareto efficient which is consistent with those of a weighted sum optimal control problem, and give the expressions of all Pareto efficient strategies.