English
Related papers

Related papers: Optimal stopping problems in diffusion-type models…

200 papers

We consider an optimal stopping time problem related with many models found in real options problems. The main goal of this work is to bring for the field of real options, different and more realistic pay-off functions, and negative…

Optimization and Control · Mathematics 2017-01-10 Manuel Guerra , Cláudia Nunes , Carlos Oliveira

We study the problem of optimal stopping of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a…

Optimization and Control · Mathematics 2023-01-10 Nacira Agram , Bernt Oksendal

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

We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…

Computational Finance · Quantitative Finance 2017-07-04 Maria do Rosario Grossinho , Yaser Faghan Kord , Daniel Sevcovic

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

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…

Probability · Mathematics 2012-04-17 Andreas E. Kyprianou , Curdin Ott

This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…

Probability · Mathematics 2025-09-01 Zbigniew Palmowski , Paweł Stȩpniak

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

In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can…

Numerical Analysis · Mathematics 2021-11-02 Sebastian Becker , Patrick Cheridito , Arnulf Jentzen

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…

Optimization and Control · Mathematics 2025-12-30 Mathieu Laurière , Mehdi Talbi

We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is described by Ito's equation, and the number of risky assets can be…

Probability · Mathematics 2008-12-02 Nikolai Dokuchaev

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…

Pricing of Securities · Quantitative Finance 2010-11-17 Marie Bernhart , Peter Tankov , Xavier Warin

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…

Probability · Mathematics 2022-01-07 Zuo Quan Xu , Xun Yu Zhou

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

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

The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the…

Optimization and Control · Mathematics 2012-03-16 Erhan Bayraktar , Hao Xing

The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…

Probability · Mathematics 2025-05-27 Neofytos Rodosthenous , Mihail Zervos

We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…

Mathematical Finance · Quantitative Finance 2017-11-09 Maria do Rosario Grossinho , Yaser Kord Faghan , Daniel Sevcovic

Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal…

Probability · Mathematics 2019-09-24 Fabián Crocce , Ernesto Mordecki

We study the barrier that gives the optimal time to exercise an American option written on a time-dependent Ornstein--Uhlenbeck process, a diffusion often adopted by practitioners to model commodity prices and interest rates. By framing the…

Probability · Mathematics 2024-06-12 Abel Azze , Bernardo D'Auria , Eduardo García-Portugués