In this paper we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider. MSC2010 : 60G51, 60H40, 60H10, 60HXX, 93E20

In this paper we examine the relationship between the firm's investments in design quality improvement and its ability to thrive or even survive in an oligopolistic setting. We start by providing the contextual background for our approach, and then proceed to formulate a differential game theory model with six stateand two control-variables for each duopolist. More specifically, we blend a gene...

Stochastic differential games are considered in a non-Markovian setting. Typically, in stochastic differential games the modulating process of the diffusion equation describing the state flow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB met...

We present a novel trajectory optimization framework to address the issue of robustness, scalability and efficiency in optimal control and reinforcement learning. Based on prior work in Cooperative Stochastic Differential Game (CSDG) theory, our method performs local trajectory optimization using cooperative controllers. The resulting framework is called Cooperative Game-Differential Dynamic Pr...

We propose a stochastic model in evolutionary game theory where individuals (or subpopulations) can mutate changing their strategies randomly (but rarely) and explore the external environment. This environment affects the selective pressure by modifying the payoff arising from the interactions between strategies. We derive a Fokker-Plank integro-differential equation and provide Monte-Carlo sim...

We consider in this paper a class of risk-sensitive stochastic nonzero-sum differential games with parameterized nonlinear dynamics and parameterized cost functions. The parametrization is such that if all or some of the parameters are set equal to some nominal values, then the differential game either becomes equivalent to a risk-sensitive stochastic control (RSSC) problem, or decouples into s...

Autonomous aerial vehicles play an important role in military applications such as in search, surveillance and reconnaissance. Multi-player stochastic pursuit–evasion (PE) differential game is a natural model for such operations involving intelligent moving targets with uncertainties. In this paper, some fundamental issues of stochastic PE games are addressed. We first model a general stochasti...

We give a concise introduction to risk sensitive control of Markov diffusion processes and related two-controller, zero-sum differential games. The method of dynamic programming for the risk sensitive control problem leads to a nonlinear partial differential equation of HamiltonJacobi-Bellman type. In the totally risk sensitive limit, this becomes the Isaacs equation for the differential game. ...

By means of a simulated funding-agency/supported-firm stochastic dynamic game, this paper shows that the level of the subsidy provided by a funding (public) agency, normally used to correct for firm R&D shortage, might be severely underprovided. This is due to the "externalities" generated by the agency-firm strategic relationship, as showed by comparing two versions of the model: one assuming ...

An open-loop two-person zero-sum linear quadratic (LQ for short) stochastic differential game is considered. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weighting matrices in the payoff/cost functional are not assumed to be definite/nonsingular, and the cross-terms between two controls are allowed to appear. A forward-backward s...