相关论文: A Proof of the Bomber Problem's Spend-It-All Conje…

Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…

The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic…

This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…

We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or…

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…

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…

In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller…

In this article, we give an in-depth analysis of the problem of optimising the total population size for a standard logistic-diffusive model. This optimisation problem stems from the study of spatial ecology and amounts to the following…

$ \newcommand{\Re}{\mathbb{R}} \newcommand{\reals}{\mathbb{R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\optX}[1]{#1^\star} \newcommand{\Qopt}{\Mh{\optX{Q}}} \newcommand{\rad}{r} \newcommand{\Mh}[1]{#1} \newcommand{\query}{q}…

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…

Border's theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known…

We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all $K$ arms. We give an algorithm using $O(1)$ words of space with regret \[ \sum_{i=1}^{K}\frac{1}{\Delta_i}\log…

The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…

In this paper we investigate a class of swing options with firm constraints in view of the modeling of supply agreements. We show, for a fully general payoff process, that the premium, solution to a stochastic control problem, is concave…

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…

Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…

We consider a stochastic bandit problem with a possibly infinite number of arms. We write $p^*$ for the proportion of optimal arms and $\Delta$ for the minimal mean-gap between optimal and sub-optimal arms. We characterize the optimal…

There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary…

We consider predictions of the random number and the magnitude of each iid component in a random sum based on its distributional structure, where only a total value of the sum is available and where iid random components are non-negative.…

We consider the problem of computing, for a detector surface waiting for a quantum particle to arrive, the probability distribution of the time and place at which the particle gets detected, from the initial wave function of the particle in…