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We investigate a class of zero-sum linear-quadratic stochastic differential games on a finite time horizon governed by multiscale state equations. The multiscale nature of the problem can be leveraged to reformulate the associated…
In this work we study the stochastic recursive control problem, in which the aggregator (or called generator) of the backward stochastic differential equation describing the running cost is continuous but not necessarily Lipschitz with…
The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic…
We describe how to apply adjoint sensitivity methods to backward Monte-Carlo schemes arising from simulations of particles passing through matter. Relying on this, we demonstrate derivative based techniques for solving inverse problems for…
We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the…
Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics, defense, energy systems and etc. However, compared to single-agent control problems, the…
This work investigates continuous time stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. The control processes are…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…
The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle…
In this paper, we consider a deterministic dynamic programming model, and derive the envelope theorem using the Clarke differential. Compared with previous research, we do not require differentiability, convexity, or boundedness.
We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…
Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…
This article presents the variant of the approach introduced in the recent work of Bensoussan, Wong, Yam and Yuan [13] to the generic first-order mean field game problem. A major contribution here is the provision of new crucial a priori…
This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D. The…
First, we study the existence of solutions for a class of first order mean field games systems \begin{equation*} \left\{\begin{aligned} &H(x,u,Du)=F(x,m(t)),\quad &&x\in M,\ \forall\ t\in[0,T],\\ &\partial_t…
We discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we focus on the question of existence of associated…
Leveraging tools from the study of linear fractional transformations and algebraic Riccati equations, a local characterization of consistent conjectural variations equilibrium is given for two player games on continuous action spaces with…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…