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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…
Previous authors have considered optimal stopping problems driven by the running maximum of a spectrally negative L\'evy process $X$, as well as of a one-dimensional diffusion. Many of the aforementioned results are either implicitly or…
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 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…
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…
We present a method to solve optimal stopping problems in infinite horizon for a L\'evy process when the reward function can be non-monotone. To solve the problem we introduce two new objects. Firstly, we define a random variable $\eta(x)$…
This paper studies the optimal multiple-stopping problem arising in the context of the timing option to withdraw from a project in stages. The profits are driven by a general spectrally negative Levy process. This allows the model to…
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…
This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…
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…
In the spirit of [Surya07'], we develop an average problem approach to prove the optimality of threshold type strategies for optimal stopping of L\'evy models with a continuous additive functional (CAF) discounting. Under spectrally…
We revisit a stochastic control problem of optimally modifying the underlying spectrally negative Levy process. A strategy must be absolutely continuous with respect to the Lebesgue measure, and the objective is to minimize the total costs…
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…
The optimal stopping problem for a Hunt processes on $\R$ is considered via the representation theory of excessive functions. In particular, we focus on infinite horizon (or perpetual) problems with one-sided structure, that is, there…
We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…
We provide, in a general setting, explicit solutions for optimal stopping problems that involve a diffusion process and its running maximum. Besides, a new feature includes absorbing boundaries that vary with the value of the running…
This paper studies an optimal stopping problem for L\'evy processes. We give a justification of the form of the Snell envelope using standard results of optimal stopping. We also justify the convexity of the value function, and without a…
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 revisit an absolutely-continuous version of the stochastic control problem driven by a L\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex.…
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.