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We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a…

Pricing of Securities · Quantitative Finance 2013-02-19 Luis H. R. Alvarez E. , Pekka Matomäki , Teppo A. Rakkolainen

We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by…

Probability · Mathematics 2021-05-04 Christian Bayer , Paul Hager , Sebastian Riedel , John Schoenmakers

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…

Probability · Mathematics 2021-06-25 Mine Caglar , Andreas E. Kyprianou , Ceren Vardar-Acar

We consider the representation of the value of a class of optimal stopping problems of linear diffusions in a linearized form as an expected supremum of a known function. We establish an explicit integral representation of this representing…

Probability · Mathematics 2017-03-16 Luis H. R. Alvarez E. , Pekka Matomäki

In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…

Optimization and Control · Mathematics 2025-09-04 Siyu Lv , Zhen Wu , Jie Xiong , Xin Zhang

This study considers an optimal reinsurance, investment, and dividend strategy control problem for insurance companies in a regulated Markov regime-switching environment, intending to maximize long-run average reward. Unlike existing single…

Optimization and Control · Mathematics 2025-12-18 Lingjia Zeng , Manman Li

In this paper we demonstrate that the Riesz representation of excessive functions is a useful and enlightening tool to study optimal stopping problems. After a short general discussion of the Riesz representation we concretize, firstly, on…

Probability · Mathematics 2015-10-21 Sören Christensen , Paavo Salminen

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…

Optimization and Control · Mathematics 2017-07-07 Erhan Bayraktar , Christopher W. Miller

We study optimal stopping for diffusion processes with unknown model primitives within the continuous-time reinforcement learning (RL) framework developed by Wang et al. (2020), and present applications to option pricing and portfolio…

Optimization and Control · Mathematics 2025-08-12 Min Dai , Yu Sun , Zuo Quan Xu , Xun Yu Zhou

We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the…

Probability · Mathematics 2023-09-08 M. N. M. van Lieshout

In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…

Optimization and Control · Mathematics 2020-06-23 Jinghai Shao , Kun Zhao

We consider the optimal stopping problem for a Gauss-Markov process conditioned to adopt a prescribed terminal distribution. By applying a time-space transformation, we show it is equivalent to stopping a Brownian bridge pinned at a random…

Probability · Mathematics 2025-05-26 Abel Azze , Bernardo D'Auria

In this paper we consider stopping problems for continuous-time Markov chains under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. More precisely our aim is to maximize the certainty…

Probability · Mathematics 2019-07-05 Nicole Bäuerle , Anton Popp

This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying…

Probability · Mathematics 2007-05-23 Xianping Guo , Ulrich Rieder

In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…

Probability · Mathematics 2008-12-18 Ludger Rüschendorf , Mikhail A. Urusov

We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the…

Optimization and Control · Mathematics 2009-05-25 Erhan Bayraktar , Masahiko Egami

In this paper we present a new verification theorem for optimal stopping problems for Hunt processes. The approach is based on the Fukushima-Dynkin formula, and its advantage is that it allows us to verify that a given function is the value…

Optimization and Control · Mathematics 2019-09-04 Achref Bachouch , Olfa Draouil , Bernt Øksendal

This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…

Optimization and Control · Mathematics 2016-02-16 Benoîte de Saporta , François Dufour , Christophe Nivot

The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…

Optimization and Control · Mathematics 2019-11-15 Florin Avram , Dan Goreac

We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. Optimal stopping rules are found as the…

Statistics Theory · Mathematics 2012-12-18 A. N. Shiryaev , M. V. Zhitlukhin