A variational formula for stochastic controls and some applications
Abbreviated Journal Title
Pure Appl. Math. Q.
stochastic controls; variational formula; maximum principle; differential games; minimax principle; sufficient condition; saddle; point; Nash equilibrium; MAXIMUM PRINCIPLE; DIFFERENTIAL-EQUATIONS; Mathematics, Applied; Mathematics
For a controlled stochastic differential equation with a Bolza type performance functional, a variational formula for the functional in a given control process direction is derived, by means of backward stochastic differential equations. As applications, some Pontryagin type maximum principles are established for optimal controls of control problems, for saddle points of open-loop two-person zero-sum differential games, and for Nash equilibria of N-person nonzero-sum differential games. The results presented in this paper generalizes/simplifies the relevant ones found in  . In addition, a sufficient existence condition of Nash equilibria is proved for nonzero-sum games.
Pure and Applied Mathematics Quarterly
"A variational formula for stochastic controls and some applications" (2007). Faculty Bibliography 2000s. 7448.