Related papers: Variational View to Optimal Stopping Problems for …

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…

Infinite horizon optimal stopping problems for a L\'evy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A…

We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…

We consider a new type of optimal stopping problems where the absorbing boundary moves as the state process X attains new maxima S. More specifically, we set the absorbing boundary as S-b where b is a certain constant. This problem is…

This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule…

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.

We study optimal design problems for stationary diffusion involving one or more state equations and mixtures of an arbitrary number of anisotropic materials. Since such problems typically do not admit classical solutions, we adopt a…

We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.

I consider a stochastic optimization problem for a time-changed Bessel process whose diffusion rate is constrained to be between two positive values $r_{1}<r_{2}$. The problem is to find an optimal adapted strategy for the choice of…

Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers…

We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…

Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary…

The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionless materials. Such models and their mathematical…

We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…

We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

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…

The purpose of this paper is two-fold: We extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori…

In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…

In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the asymptotic behavior of its solutions, and prove the…