Related papers: Time-inconsistent mean-field optimal stopping: A l…
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…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
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…
In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on current state and an entropy-regularized term is added to the reward functional. Such a…
In this paper, we introduce a non-linear Snell envelope which at each time represents the maximal value that can be achieved by stopping a BSDE with constrained jumps. We establish the existence of the Snell envelope by employing a…
Let $X$ be a one-dimensional diffusion and let $g\colon[0,T]\times\mathbb{R}\to\mathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent…
This paper is concerned with optimal switching over multiple modes in continuous time and on a finite horizon. The performance index includes a running reward, terminal reward and switching costs that can belong to a large class of…
We study an infinite horizon optimal stopping problem which arises naturally in the optimal timing of a firm/project sale or in the valuation of natural resources: the functional to be maximised is a sum of a discounted running reward and a…
We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…
Given an initial (resp., terminal) probability measure $\mu$ (resp., $\nu$) on $\mathbb{R}^d$, we characterize those optimal stopping times $\tau$ that maximize or minimize the functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$,…
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed…
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…
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…
This paper analyzes the convergence of the finite population optimal stopping problem towards the corresponding mean field limit. Building on the viscosity solution characterization of the mean field optimal stopping problem of our previous…
In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $\delta$, the so called refraction period. This prevents the optimal exercise times…
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…
This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…
In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller--Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have…
We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a…
The optimal stopping problem for a Hunt processes on $\R$ is considered via the representation theory of excessive functions. In particular, we focus on infinite horizon (or perpetual) problems with one-sided structure, that is, there…