Related papers: Contraction options and optimal multiple-stopping …

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…

We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The…

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…

We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative L\'evy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first…

We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a…

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…

We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We…

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 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…

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…

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…

We consider an optimal dividend problem with transaction costs where the surplus is modelled by a spectrally negative L\'evy process in an Omega model. n this model, the surplus is allowed to spend time below the critical ruin level, but is…

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 adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…

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…

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…

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…

The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative Levy process until the passage time of a given level. Their marginal distributions up to an independent exponential time are also…

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $\delta$, the so called refraction period. This prevents the optimal exercise times…

For spectrally negative L\'evy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find…