Related papers: On the One-Dimensional Optimal Switching Problem
This paper studies the problem of optimal switching for one-dimensional diffusion, which may be regarded as sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of…
In this paper, we propose a direct solution method for optimal switching problems of one-dimensional diffusions. This method is free from conjectures about the form of the value function and switching strategies, or does not require the…
The principle of smooth fit is probably the most used tool to find solutions to optimal stopping problems of one-dimensional diffusions. It is important, e.g., in financial mathematical applications to understand in which kind of models and…
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.…
Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…
This article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using…
We consider a one-dimensional diffusion which solves a stochastic differential equation with Borel-measurable coefficients in an open interval. We allow for the endpoints to be inaccessible or absorbing. Given a Borel-measurable function…
We study an optimal switching problem with a state constraint: the controller is only allowed to choose strategies that keep the controlled diffusion in a closed domain. We prove that the value function associated with this problem is the…
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
We consider the optimal stopping problem consisting in, given a strong Markov process, a reward function and a discount rate, finding the stopping time such that the expected reward at the stopping time is maximum. The approach we follow,…
This paper aims to study the relationship between the maximum principle and the dynamic programming principle for recursive optimal control problem of stochastic evolution equations, where the control domain is not necessarily convex and…
We address the problem of making a managerial decision when the investment project is subsidized, which results in the resolution of an infinite-horizon optimal stopping problem of a switching diffusion driven by either an homogeneous or an…
In the paper "Dynkin Games Via Dirichlet Forms and Singular Control of One-Dimensional Diffusion", the authors tried to show the existences of a smooth value function and an optimal policy to a one-dimensional stochastic singular control…
This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the…
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…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…