Related papers: Dynamic Programming Principle for Stochastic Recur…
In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for forward-backward control system under consistent convex expectation dominated by G-expectation. Under the smooth assumptions…
In this paper, we consider state and control path-dependent stochastic zero-sum differential games, where the dynamics and the running cost include both state and control paths of the players. Using the notion of nonanticipative strategies,…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
This paper deals with the stochastic control of nonlinear systems in the presence of state and control constraints, for uncertain discrete-time dynamics in finite dimensional spaces. In the deterministic case, the viability kernel is known…
In optimal control problems defined on stratified domains, the dynamics and the running cost may have discontinuities on a finite union of submanifolds of RN. In [8, 5], the corresponding value function is characterized as the unique…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…
We analyze a stochastic optimal control problem, where the state process follows a McKean-Vlasov dynamics and the diffusion coefficient can be degenerate. We prove that its value function V admits a nonlinear Feynman-Kac representation in…
We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a…
This paper is concerned with an optimal control problem for a forward-backward stochastic differential equation (FBSDE, for short) with a recursive cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for…
This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…
We extend the work on optimal investment and consumption of a population considered in [2] to a general stochastic setting over a finite time horizon. We incorporate the Cobb-Douglas production function in the capital dynamics while the…
This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in…
We introduce a regulated stochastic diffusion model for the recycling rate and formulate a joint control problem over production and process innovation via the dynamics of recycling investment and product pricing. The resulting stochastic…
In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of a bank's work is described in this paper. The problem…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We define a model of a system that deteriorate as a result of (i) shocks, modeled as a compound Poisson process and (ii) deterministic, state dependent progressive rate, with variable and fixed maintenance cost. We define maintenance…
Growth models with internal habit formation have been studied in various settings under the assumption of deterministic dynamics. The purpose of this paper is to explore a stochastic version of the model in Carroll et al. [1997, 2000], one…
In this paper we study an optimization problem in which the control is information, more precisely, the control is a $\sigma$-algebra or a filtration. In a dynamic setting, we establish the dynamic programming principle and the law…
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…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…