We provide a very brief introduction to typical paths and the corresponding Itô type integration. Relying on this robust integration, we prove an existence uniqueness result for one-dimensional differential equations driven by with non-Lipschitz continuous coefficients in spirit of Yamada–Watanabe as well approximation Doss–Sussmann.

abstract today, debt stabilization in an uncertain environment is an important issue. in particular, the question how fiscal and monetary authorities should deal with this uncertainty is of much importance. especially for some developing countries such as iran, in which on average 60 percent of government revenues comes from oil, and consequently uncertainty about oil prices has a large effect ...

We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some second order Hamilton-Jacobi equation. Key-words : stochastic differential game, asymmetric information, viscosity solution. A.M.S. classification : 49N70, 49L...

As it is well known in differential games, the open-loop Nash equilibrium (OLNE) concept with an infinite period of commitment is weakly time-consistent but not strongly time-consistent. On the other hand, the feedback Nash equilibrium (FBNE) is Markov perfect by construction and thus a more satisfactory solution concept, but solutions are usually very difficult to derive. Explicit solutions ca...

We discuss the calculation of discriminating kernel for the discrete-time dynamic game and continuous-time dynamic game (namely differential game) using the viability kernel and reachable set. For the discrete-time dynamic game, we give an approximation of the viability kernel by the maximal reachable set. Then, based on the relationship between viability and discriminating kernels, we propose ...

We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player’s priority value satisfies a weak dynamic programming principle and thus solves the associated fully non-linear partial differential equation in the viscosity sense.

In this Note, assuming that the generator is uniform Lipschitz in the unknown variables, we relate the solution of a one dimensional backward stochastic differential equation with the value process of a stochastic differential game. Under a domination condition, an Fconsistent evaluations is also related to a stochastic differential game. This relation comes out of a min-max representation for ...

In this paper, we initiate a study on optimal control problem for stochastic differential games under generalized expectation via backward stochastic differential equations and partial information. We first prove a sufficient maximum principle for zero-sum stochastic differential game problem. And then extend our approach to general stochastic differential games (nonzero–sum games), and obtain ...

We study a bifurcation problem for a system of two differential equations in implicit form. For each value of the parameter θ, the solution yields a pair of Nash equilibrium strategies in feedback form, for a non-cooperative differential game. When θ = 0, the second player has no power to influence the dynamics of the system, and his optimal strategy is myopic. The game thus reduces to an optim...