相关论文: On the Basis of the Hamilton-Jacobi-Bellman Equati…

We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…

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 introduce Hamilton-Jacobi-Bellman (HJB) equations for Q-functions in continuous time optimal control problems with Lipschitz continuous controls. The standard Q-function used in reinforcement learning is shown to be the…

We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky…

We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we…

We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only…

The aim of this work is to present the regularity condition (also known in the literature as structure condition) an integro-differential operator may satisfy in order for the domination principle to hold for (sub-,super-) solutions of…

An example of a nonunique solution of the Cauchy problem of Hamilton-Jacobi-Bellman (HJB) equation with surprisingly regular Hamiltonian is presented. The Hamiltonian H(t,x,p) is locally Lipschitz continuous with respect to all variables,…

In this paper, we study the existence and uniqueness of viscosity solutions to a kind of Hamilton-Jacobi-Bellman (HJB) equations combined with algebra equations. This HJB equation is related to a stochastic optimal control problem for which…

We study a consumption-investment problem in a multi-asset market where the returns follow a generic rank-based model. Our main result derives an HJB equation with Neumann boundary conditions for the value function and proves a…

This study investigates an optimal investment problem for an insurance company operating under the Cramer-Lundberg risk model, where investments are made in both a risky asset and a risk-free asset. In contrast to other literature that…

We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a…

The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately,…

The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton-Jacobi-Bellman (HJB) equation. A…

This paper extends the classical consumption and portfolio rules model in continuous time (Merton 1969, 1971) to the framework of decision-makers with time-inconsistent preferences. The model is solved for different utility functions for…

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…

This paper, which is the natural continuation of a previous paper by the same authors, studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes…

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…

This paper develops a framework for establishing the existence of solutions to the equilibrium Hamilton-Jacobi-Bellman (EHJB) equation arising in time-inconsistent stochastic control problems. The time-inconsistency in our setting arises…