Related papers: A singular infinite dimensional Hamilton-Jacobi-Be…
This paper establishes the existence and uniqueness of mild solutions to stationary Hamilton-Jacobi-Bellman (HJB) equations associated with infinite-horizon stochastic optimal control problems in separable Hilbert spaces. Our framework…
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms…
The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple time horizons, or when the time horizon is not known in…
We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the…
In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider the cause of this…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
We prove local (in time) existence and uniqueness for a class of infinite-dimensional Nash systems, namely systems of infinitely many Hamilton-Jacobi-Bellman equations set in an infinite-dimensional Euclidean space. Such systems have been…
This investigation is dedicated to a two-player zero-sum stochastic differential game (SDG), where a cost function is characterized by a backward stochastic differential equation (BSDE) with a continuous and monotonic generator regarding…
We study a two-player zero-sum stochastic differential game with asymmetric information where the payoff depends on a controlled continuous-time Markov chain X with finite state space which is only observed by player 1. This model was…
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…
This paper investigates the well-posedness of a type of state constraint ergodic Mean Field Game system in a bounded domain in which the Hamilton-Jacobi-Bellman equation is paired with an infinite Dirichlet boundary condition. In this…
We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law. The dynamical systems under consideration…
Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is…
We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and…
This paper introduces a class of continuous-time, finite-player stochastic general-sum differential games that admit solutions through an exact linear PDE system. We formulate a distribution planning game utilizing the cross-log-likelihood…
We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation of the game turns out to be a…