Related papers: Impulse control of conditional McKean-Vlasov jump …
We discuss the optimal Markovian coupling before an exponential time of the Kolmogorov diffusion, and a class of related stochastic control problems in which the aim is to hit the origin before an exponential time. We provide a scaling…
We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…
Throughout this paper, we focused our aim on the problem of optimal control under a risk-sensitive performance functional, where the system is given by a fully coupled forward-backward stochastic differential equation with jump. The risk…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
This paper concerns an optimal control problem $(P)$ related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem $(P_S)$ for a McKean-Vlasov equation. The existence of an optimal…
We consider the impulse control of Levy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or…
In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum…
We consider a Markovian jumping process which is defined in terms of the jump-size distribution and the waiting-time distribution with a position-dependent frequency, in the diffusion limit. We assume the power-law form for the frequency.…
We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for…
We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…
We study the optimal dividend problem for a firm's manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying…
We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space.…
In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to…
The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed…
In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…
We consider an optimal control problem for a system governed by a Volterra integral equation with impulsive terms. The impulses act on both the state and the control; the control consists of switchings at discrete times. The cost functional…
We consider a class of impulse control problems for general underlying strong Markov processes on the real line, which allows for an explicit solution. The optimal impulse times are shown to be of threshold type and the optimal threshold is…
This paper analyzes a class of impulse control problems for multi-dimensional jump diffusions in the finite time horizon. Following the basic mathematical setup from Stroock and Varadhan \cite{StroockVaradhan06}, this paper first…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift,…