Catherine Rainer

Nash Equilibrium Payoffs for Nonzero-Sum Stochastic Differential Games

Existence and characterization of Nash equilibrium payoffs are proved for stochastic nonzero-sum differential games.

Existence of stochastic control under state constraints

Abstract In this Note, we give a necessary and sufficient condition for the existence of control that keeps the corresponding trajectory of the related stochastic control system within a prescribed closed subset of the state space. The problem of existence of stochastic control under a state-constraint is also called the viability property of the underlying control system. Our result is: the square of the distance function of this constraint is a viscosity supersolution of a Hamilton-Jacobi-Bellman equation if and only if the system enjoys the viability property.

Mean-field stochastic differential equations and associated PDEs

In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data

Existence of an optimal control for stochastic control systems with nonlinear cost functional

(t,x)\in[0,T]\times R^d,

Games with incomplete information in continuous time and for continuous types

which coefficients depend on both the solution

Markov Games with Frequent Actions and Incomplete Information

X^{t,x}_s

Markov Games with Frequent Actions and Incomplete Information—The Limit Case

but also its law. By considering square integrable random variables

Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton-Jacobi Equations with Superquadratic Growth in the Gradient

\xi

Differential games with asymmetric information and without Isaacs’ condition

as initial condition for this equation, we can easily show the flow property of the solution

Pathwise strategies for stochastic differential games with an erratum to ''Stochastic Differential Games with Asymmetric Information''

X^{t,\xi}_s