Related papers: An optimal stopping problem for spectrally negativ…
This paper concerns optimal stopping problems driven by the running maximum of a spectrally negative L\'{e}vy process $X$. More precisely, we are interested in modifications of the Shepp-Shiryaev optimal stopping problem [Avram, Kyprianou…
This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Levy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem, which has its…
Given a spectrally negative L\'evy process $X$ drifting to infinity, (inspired on the early ideas of Shiryaev (2002)) we are interested in finding a stopping time that minimises the $L^p$ distance ($p>1$) with $g$, the last time $X$ is…
We propose an alternative approach for solving a number of well-studied optimal stopping problems for L\'evy processes. Instead of the usual method of guess-and-verify based on martingale properties of the value function, we suggest a more…
We establish a systematic solution method for optimal stopping problems of spectrally negative L\'evy processes. Our approach relies essentially on the potential theory, in particular the Riesz decomposition and the maximum principle. Using…
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 paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller…
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 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…
We consider the optimal prediction problem of stopping a spectrally negative L\'evy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared error penalty function. Under some mild conditions,…
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,…
Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…
This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to…
We consider a class of infinite-time horizon optimal stopping problems for spectrally negative Levy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale…
This paper solves exit problems for spectrally negative Markov additive processes and their reflections. A so-called scale matrix, which is a generalization of the scale function of a spectrally negative \levy process, plays a central role…
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 describe the solution of an optimal stopping problem for a stable L\'evy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains…
We investigate the optimal stopping problems involving the supremum of a diffusion. The starting point is the link between works of Peskir and Meilijson, which we describe in a unified manner. The description developped follows mainly the…
Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…
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…