Related papers: An algorithm to solve optimal stopping problems fo…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
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.…
We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game…
In this paper, we study the optimal dividend problem under the continuous time diffusion model with the bounded dividend rate from the Reinforcement Learning (RL) perspective. Unlike the standard literature, our main focus will be on…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the…
In this paper we present a new verification theorem for optimal stopping problems for Hunt processes. The approach is based on the Fukushima-Dynkin formula, and its advantage is that it allows us to verify that a given function is the value…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We consider optimal stopping problems with finite-time horizon and state-dependent discounting. The underlying process is a one-dimensional linear diffusion and the gain function is time-homogeneous and difference of two convex functions.…
We consider the problem of optimal stopping for a one-dimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0,\infty],…
We study optimal stopping for diffusion processes with unknown model primitives within the continuous-time reinforcement learning (RL) framework developed by Wang et al. (2020), and present applications to option pricing and portfolio…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a…
In this paper we demonstrate that the Riesz representation of excessive functions is a useful and enlightening tool to study optimal stopping problems. After a short general discussion of the Riesz representation we concretize, firstly, on…
We consider the representation of the value of a class of optimal stopping problems of linear diffusions in a linearized form as an expected supremum of a known function. We establish an explicit integral representation of this representing…