Related papers: A singular infinite dimensional Hamilton-Jacobi-Be…
In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage…
We consider a class of economic growth models that includes the classical Ramsey--Cass--Koopmans capital accumulation model and verify that, under several assumptions, the value function of the model is the unique viscosity solution to the…
We study a pursuit-evasion differential game with finite number of pursuers and one evader in Hilbert space with geometric constraints on the control functions of players. We solve the game by presenting explicit strategies for pursuers…
This paper treats the Merton problem how to invest in safe assets and risky assets to maximize an investor's utility, given by investment opportunities modeled by a $d$-dimensional state process. The problem is represented by a partial…
This paper presents SIMPOL (Simplified Policy Iteration), a modular numerical framework for solving continuous-time heterogeneous agent models. The core economic problem, the optimization of consumption and savings under idiosyncratic…
The paper deals with a zero-sum differential game for a dynamical system which motion is described by a nonlinear delay differential equation under an initial condition defined by a piecewise continuous function. The corresponding Cauchy…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
We solve in mild sense Hamilton Jacobi Bellman equations, both in an infinite dimensional Hilbert space and in a Banach space, with lipschitz Hamiltonian and lipschitz continuous final condition, and asking only a weak regularizing property…
Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…
We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the…
This paper derives the Hamilton-Jacobi-Bellman equation of nonlinear optimal control problems for cost functions with fractional discount rate from the Bellman's principle of optimality. The fractional discount rate is described by…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…
In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…
In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to…
Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…
Here, we study Hamilton-Jacobi-Bellman equations on graphs. These are meant to be the analog of any of the following types of equations in the continuum setting of partial differential and nonlocal integro-differential equations:…
We consider a two-player zero-sum deterministic differential game where each player uses both continuous and impulse controls in infinite-time horizon. We assume that the impulses supposed to be of general term and the costs depend on the…
We investigate an infinite dimensional partial differential equation of Isaacs' type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity…
This survey collects, within a unified framework, various results (primarily by the authors themselves) on the use of Deterministic Infinite-Dimensional Optimal Control Theory to address applied economic models. The main aim is to…