Related papers: The inverse first-passage problem and optimal stop…
We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle…
We have developed efficient techniques to solve the first-time problems of Brownian motion. Based on a time-scale separation of recrossings, we show that Eyring's transmission coefficient ($\kappa$) equals to the one ($\kappa_\mathrm{V}$)…
Given two probability measures $\mu, \nu$ on $\mathbb{R}^d$, in subharmonic order, we describe optimal stopping times $\tau$ that maximize/minimize the cost functional $\mathbb{E} |B_0 - B_\tau|^{\alpha}$, $\alpha > 0$, where $(B_t)_t$ is…
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particles being absorbed before some final time horizon, given the…
The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the…
How can one change a system, in order to change its statistical properties in a prescribed way? In this note we consider a control problem related to the theory of linear response. Given an expanding map of the unit circle with an…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
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…
We consider a run-and-tumble particle on a finite interval $[a,b]$ with two absorbing end points. The particle has an internal velocity state that switches between three values $v,0,-v$ at exponential times, thus incorporating positive…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
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…
In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not…
First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This modifies a formula by Perry et al (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for…
We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide…
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 consider optimal transport problems where the cost is optimized over controlled dynamics and the end time is free. Unlike the classical setting, the search for optimal transport plans also requires the identification of optimal "stopping…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions,…