Related papers: Two-sided optimal stopping for L\'evy processes
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of…
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…
Let X_t, 0<=t<=T be a one-dimensional stochastic process with independent and stationary increments. This paper considers the problem of stopping the process X_t "as close as possible" to its eventual supremum M_T:=sup{X_t: 0<=t<=T}, when…
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 study two-armed Levy bandits in continuous-time, which have one safe arm that yields a constant payoff s, and one risky arm that can be either of type High or Low; both types yield stochastic payoffs generated by a Levy process. The…
We prove sharp two-sided estimates on the tail probability of the first hitting time of bounded interval as well as its asymptotic behaviour for general non-symmetric processes which satisfy an integral condition \[ \int_0^{\infty}…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…
This paper provides a multivariate extension of Bertoin's pathwise construction of a L\'evy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original…
In this paper, we study the $m$-states optimal switching problem in finite horizon, when the switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central evaluation in cases…
We develop a theory of optimal stopping problems under G-expectation framework. We first define a new kind of random times, called G-stopping times, which is suitable for this problem. For the discrete time case with finite horizon, the…
In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we…
We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse…
We study a stochastic control problem where the underlying process follows a spectrally negative L\'{e}vy process. A controller can continuously increase the process but only decrease it at independent Poisson arrival times. We show the…
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…
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…
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of…
In this paper, we study the optimal stopping problem in the case where the reward is given by a family $(\phi(\tau ),\;\;\tau \in \stopo)$ of non negative random variables indexed by predictable stopping times. We treat the problem by means…
We study optimal stopping of Feller-Markov processes to maximise an undiscounted functional consisting of running and terminal rewards. In a finite-time horizon setting, we extend classical results to unbounded rewards. In infinite horizon,…