Related papers: Explicit solutions in one-sided optimal stopping p…
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…
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 study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values…
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…
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…
A finite horizon optimal stopping problem for an infinite dimensional diffusion $X$ is analyzed by means of variational techniques. The diffusion is driven by a SDE on a Hilbert space $\mathcal{H}$ with a non-linear diffusion coefficient…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…
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 introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
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 provide, in a general setting, explicit solutions for optimal stopping problems that involve diffusion process and its running maximum. Our approach is to use the excursion theory for Levy processes. Since general diffusions are, in…
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…
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…
We investigate optimal stopping problems for systems driven by the Brownian sheet. Our analysis is divided into two parts. In the first part we derive explicit solutions to two optimal stopping problems for the exponentially discounted…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…
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…
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 consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…