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We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…

Probability · Mathematics 2013-06-20 V. I. Arkin , A. D. Slastnikov

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.

Optimization and Control · Mathematics 2011-01-11 Erhan Bayraktar , Song Yao

We study zero-sum stochastic games between a singular controller and a stopper when the (state-dependent) diffusion matrix of the underlying controlled diffusion process is degenerate. In particular, we show the existence of a value for the…

Optimization and Control · Mathematics 2024-07-15 Andrea Bovo , Tiziano De Angelis , Jan Palczewski

A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…

Optimization and Control · Mathematics 2020-01-23 Sören Christensen , Kristoffer Lindensjö

We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a non-exponential (weighted) discount function. In particular, we study (weak)…

Probability · Mathematics 2022-07-01 Andi Bodnariu , Sören Christensen , Kristoffer Lindensjö

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…

Robotics · Computer Science 2016-12-08 Emmanuel Boidot , Aude Marzuoli , Eric Feron

Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…

Optimization and Control · Mathematics 2020-11-04 Krzysztof Szajowski

We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum…

Probability · Mathematics 2017-05-11 Miryana Grigorova , Marie-Claire Quenez

We consider a class of zero-sum stopper vs. singular-controller games in which the controller can only act on a subset $d_0<d$ of the $d$ coordinates of a controlled diffusion. Due to the constraint on the control directions these games…

Optimization and Control · Mathematics 2024-02-02 Andrea Bovo , Tiziano De Angelis , Jan Palczewski

In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…

Optimization and Control · Mathematics 2025-03-05 Andrea Cosso , Laura Perelli

We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…

Computational Finance · Quantitative Finance 2012-10-10 Timothy C. Johnson

We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear…

Optimization and Control · Mathematics 2014-11-13 Tiziano De Angelis , Giorgio Ferrari

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…

Probability · Mathematics 2009-11-23 Erhan Bayraktar , Ioannis Karatzas , Song Yao

We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…

Optimization and Control · Mathematics 2025-06-24 Václav E. Beneš , Georgy Gaitsgori , Ioannis Karatzas

We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…

Optimization and Control · Mathematics 2010-01-20 Mike Ludkovski

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…

Mathematical Finance · Quantitative Finance 2014-12-16 Denis Belomestny , Volker Kraetschmer

We consider the non-linear optimal multiple stopping problem under general conditions on the non-linear evaluation operators, which might depend on two time indices: the time of evaluation/assessment and the horizon (when the reward or loss…

Optimization and Control · Mathematics 2025-04-21 Miryana Grigorova , Marie-Claire Quenez , Peng Yuan

We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…

Probability · Mathematics 2015-05-08 Luis H. R. Alvarez E. , Pekka Matomäki

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…

Probability · Mathematics 2026-01-09 Alexander Gnedin

This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the $d$-dimensional Wiener process. We first obtain some verification theorems for…

Probability · Mathematics 2016-11-04 Sören Christensen , Fabián Crocce , Ernesto Mordecki , Paavo Salminen