Related papers: Geometry of Distribution-Constrained Optimal Stopp…
The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy…
The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb {E}[c(X_1,X_2)]$ by varying the joint distribution $(X_1,X_2)$ where the marginal distributions of the random variables $X_1$ and $X_2$ are…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…
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.…
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved…
This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs. Using an auxiliary function of maximum representation type, conditions are given to…
We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…
The scope of this paper is to study the optimal stopping problems associated to a stochastic process, which may represent the gain of an investment, for which information on the final value is available a priori. This information may…
Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…
The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established.…
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…
The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod…
We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field…
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…
In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Le\~ao, Ohashi and Russo and, in contrast to previous works, our methodology…
We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set…
In classical optimal transport, the contributions of Benamou-Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas.…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…