We study how continuous time Bertrand and Cournot competitions, in which firms producing similar goods compete with one another by setting prices or quantities respectively, can be analyzed as continuum dynamic mean field games. Interactions are of mean field type in the sense that the demand faced by a producer is affected by the others through their average price or quantity. Motivated by ene...

Optimal investment and consumption problem for a CRRA investor or agent is solved in this study. An invests the financial market with one risk-free security risky security. The stochastic interest rate dynamics of follow Ho-Lee model modeled as Heston’s its volatility parameter following Cox-Ingersoll-Ross (CIR) model. Interest rates rates, reality, are due to uncertain events such Coronavirus ...

Recent work on path integral stochastic optimal control theory Theodorou et al. (2010a); Theodorou (2011) has shown promising results in planning and control of nonlinear systems in high dimensional state spaces. The path integral control framework relies on the transformation of the nonlinear Hamilton Jacobi Bellman (HJB) partial differential equation (PDE) into a linear PDE and the approximat...

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and HJB inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJ...

We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of the Hamilton Jacobi Bellman (HJB) equation which is a highly non linear partia...

The goal of this paper is to study a singular perturbation problem in the framework of optimal control on multi-domains. We consider an optimal control problem in which the controlled system contains a fast and a slow variables. This problem is reformulated as an Hamilton-JacobiBellman (HJB) equation. The main difficulty comes from the fact that the fast variable lives in a multi-domain. The ge...

We consider the numerical solution of discretised Hamilton-Jacobi-Bellman (HJB) equations with applications in finance. For the discrete linear complementarity problem arising in American option pricing, we study a policy iteration method. We show, analytically and numerically, that, in standard situations, the computational cost of this approach is comparable to that of European option pricing...

This paper draws on two sources of motivation: (1) The European Union Emission Trading Scheme (EU-ETS) aims at limiting the overall emissions of greenhouse gases. The optimal abatement strategy of companies for the use of emission permits can be described as the viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is a question of general interest, how regulatory constraints can b...