We present a full and corrected proof of the stochastic verification theorem that was first obtained by X. Y. Zhou, J. Yong and X. Li, Stochastic Verification theorems within the framework of viscosity solutions, SIAM J. Control Optim., 35 (1997), pp. 243–253.

In this article, we consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, which consists in imposing the “boundary conditions” in the whole complementary of the domain. We are looking for conditions on the differential and integral parts of the equation in order to ensure that the Dirichlet boundary condition is satisfied in the classical sense...

I provide a full characterization of the quality choice in duopolies with vertical differentiation, without assuming ex-ante if the market is fully covered or not. This will allow to show that covered or uncovered market configurations are endogenous outcomes of firms’ strategic interaction. To this purpose, I assume that firms are characterized by quadratic fixed costs of quality improvements ...

In this paper, we deal with a class of backward stochastic differential equations driven by Teugels martingales associated with a Lévy process (BSDELs). The comparison theorem is obtained. It is also shown that the solution of BSDE provides a viscosity solution of the associated system with partial integro-differential equations.

In this paper we use viscosity solution methods to show that almost integrable Hamiltonian systems are not smoothly integrable at rotation numbers which are exponentially close to resonances.

In this paper we show how to use a Tug-of-War game to obtain existence of a viscosity solution to the infinity laplacian with nonhomogeneous mixed boundary conditions. For a Lipschitz and positive function g there exists a viscosity solution of the mixed boundary value problem,

This poster will describe the security problems of the emerging vehicular networks. It will also outline the solution architecture and several of its components.

We present a generalization of Zubov’s method to perturbed differential equations. The goal is to characterize the domain of attraction of a set which is uniformly locally asymptotically stable under all admissible time varying perturbations. We show that in this general setting the straightforward generalization of the classical Zubov’s equations has a unique viscosity solution which character...