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Related papers: Optimal stopping under probability distortion

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We investigate optimal stopping problems for systems driven by the Brownian sheet. Our analysis is divided into two parts. In the first part we derive explicit solutions to two optimal stopping problems for the exponentially discounted…

Probability · Mathematics 2026-03-16 Nacira Agram , Bernt Oksendal , Frank Proske , Olena Tymoshenko

We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…

Probability · Mathematics 2015-08-06 V. I. Arkin , A. D. Slastnikov

This paper studies explicitly solvable multidimensional optimal stopping problems of sum- and product-type in discrete and continuous time using the monotone case approach. It gives a review on monotone case stopping using the Doob…

Probability · Mathematics 2019-06-04 Sören Christensen , Albrecht Irle

We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…

Optimization and Control · Mathematics 2017-02-15 Magnus Perninge

In this paper we consider a connection between the famous Skorohod embedding problem and the Shiryaev inverse problem for the first hitting time distribution of a Brownian motion: given a probability distribution, $F$, find a boundary such…

Probability · Mathematics 2011-11-01 Sebastian Jaimungal , Alexander Kreinin , Angel Valov

In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…

Systems and Control · Electrical Eng. & Systems 2024-10-08 Fengjiao Liu , George Rapakoulias , Panagiotis Tsiotras

The purpose of this paper is two-fold: We extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori…

Optimization and Control · Mathematics 2021-04-28 Nacira Agram , Sven Haadem , Bernt Oksendal , Frank Proske

We consider the hedging error of a derivative due to discrete trading in the presence of a drift in the dynamics of the underlying asset. We suppose that the trader wishes to find rebalancing times for the hedging portfolio which enable him…

Probability · Mathematics 2014-07-18 Jiatu Cai , Masaaki Fukasawa , Mathieu Rosenbaum , Peter Tankov

We study several optimal stopping problems that arise from trading a mean-reverting price spread over a finite horizon. Modeling the spread by the Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i) the long-short…

Trading and Market Microstructure · Quantitative Finance 2017-01-12 Tim Leung , Yerkin Kitapbayev

In the classical quickest detection problem, one must detect as quickly as possible when a Brownian motion without drift "changes" into a Brownian motion with positive drift. The change occurs at an unknown "disorder" time with exponential…

Probability · Mathematics 2015-05-29 Robert C. Dalang , Albert N. Shiryaev

We define a class of reflected backward stochastic differential equation (RBSDE) driven by a marked point process (MPP) and a Brownian motion, where the solution is constrained to stay above a given c\`adl\`ag process. The MPP is only…

Probability · Mathematics 2017-09-28 Nahuel Foresta

Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…

Probability · Mathematics 2022-05-19 Martin Redmann

We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…

Mathematical Finance · Quantitative Finance 2023-12-13 Peter Bank , Yan Dolinsky

We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…

Mathematical Finance · Quantitative Finance 2018-04-23 Peter Bank , Moritz Voß

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…

Probability · Mathematics 2015-09-03 Erik Ekström , Juozas Vaicenavicius

We consider a mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular…

Probability · Mathematics 2008-12-18 Vathana Ly Vath , Huyên Pham , Stéphane Villeneuve

We present a numerical method to compute the optimal maintenance time for a complex dynamic system applied to an example of maintenance of a metallic structure subject to corrosion. An arbitrarily early intervention may be uselessly costly,…

Probability · Mathematics 2015-03-17 Benoîte de Saporta , François Dufour , Huilong Zhang , Charles Elegbede

Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In this note we make such an embedding explicit by means of a…

Probability · Mathematics 2020-02-04 Giang T. Nguyen , Oscar Peralta

The subject of this work has its roots in the so called Schroedginer Bridge Problem (SBP) which asks for the most likely distribution of Brownian particles in their passage between observed empirical marginal distributions at two distinct…

Systems and Control · Computer Science 2016-08-15 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon

In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…

Probability · Mathematics 2017-08-04 Vicky Henderson , David Hobson , Matthew Zeng