Related papers: Two-sided optimal stopping for L\'evy processes

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.…

It is proved that the two-sided exits of a Levy process are proper, i.e. not a.s. equal to their one-sided counterparts, if and only if said process is not a subordinator or the negative of a subordinator. Furthermore, Levy processes are…

We consider the optimal double stopping time problem defined for each stopping time $S$ by $v(S)=\esssup\{E[\psi(\tau_1, \tau_2) | \F_S], \tau_1, \tau_2 \geq S \}$. Following the optimal one stopping time problem, we study the existence of…

Consider the discounted optimal stopping problem for a real valued Markov process with only positive jumps. We provide a theorem to verify that the optimal stopping region has the form {x >= x^*} for some critical threshold x^*, and a…

We study an optimal process control problem with multiple assignable causes. The process is initially in-control but is subject to random transition to one of multiple out-of-control states due to assignable causes. The objective is to find…

In this paper we study the optimal stopping problem for L\'evy processes studied by Novikov and Shiryayev, Stochastics, 2007 In particular, we are interested in finding the representing measure of the value function. It is seen that that…

We consider a L\'evy process that starts from $x<0$ and conditioned on having a positive maximum. When Cram\'er's condition holds, we provide two weak limit theorems as $x\to -\infty$ for the law of the (two-sided) path shifted at the first…

We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…

We study decision timing problems on finite horizon with Poissonian information arrivals. In our model, a decision maker wishes to optimally time her action in order to maximize her expected reward. The reward depends on an unobservable…

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 consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…

We consider controlling the paths of a spectrally negative L\'evy process by two means: the subtraction of `taxes' when the process is at an all-time maximum, and the addition of `bailouts' which keep the value of the process above zero. We…

In this paper, we present the testing of four hypotheses on two streams of observations that are driven by L\'evy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each sensor…

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…

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 consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell…

We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…

This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…

Our purpose is to study a particular class of optimal stopping problems for Markov processes. We justify the value function convexity and we deduce that there exists a boundary function such that the smallest optimal stopping time is the…

In this article we consider a toy example of an optimal stopping problem driven by fragmentation processes. We show that one can work with the concept of stopping lines to formulate the notion of an optimal stopping problem and moreover, to…