Zero-sum stochastic differential games and backward equations

Existence of Nash equilibrium points for Markovian non-zero-sum stochastic differential games with unbounded coefficients

“…In the case when N = 2 and J 1 + J 2 = 0, this game reduces to the well known zero-sum differential game which is well documented in several works and from several points of view (see e.g. [2], [3], [5], [6], [9], [10], [14], [15], [20] etc. and the references inside).…”

Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients

“…In the past decades, the theory of BSDEs have been extensively developed and gradually become an important tool in financial problems [2,3], stochastic control [1] and stochastic games [7] and so on. One highlight of the theory is relaxing the conditions of existence and uniqueness of the solutions.…”

Backward stochastic differential equations with oblique reflection and local Lipschitz drift

“…This theory has found a wide field of applications as in stochastic optimal control and stochastic games (see Hamadène and Lepeltier [9]), in mathematical finance via the theory of hedging and nonlinear pricing theory for imperfect markets (see El Karoui et al [6]). Backward stochastic differential equations also appear to be a powerful tool for constructing Γ−martingales on manifolds (see Darling [4]).…”