A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber
Journal Title: Mathematica Applicanda. Annales Societatis Mathematicae Polonae Series III . - Year 2017, Vol 45, Issue 1
Abstract
The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. The Bruss-Weber problems we consider center around the following model: Let X1,X2, . . . ,Xn be a sequence of independent and identically distributed random variables which can take three values: {+1,−1, 0}. The goal is to maximize the probability of stopping on a value +1 or −1 appearing for the last time in the sequence. We study related problems both in discrete and continuous time settings, with known or unknown number of observations, and known and unknown probability measure. In particular, so called x-strategy with incomplete information is taken into consideration. Our contribution in the present paper is a refined analysis of several problems in this class and a study of the asymptotic behaviour of solutions. We also present simulations of the corresponding complete selection algorithms.
Authors and Affiliations
Guy Louchard
Keywords
Related Articles
- EP ID EP420944
- DOI 10.14708/ma.v45i2.4376
- Views 72
- Downloads 0
Markov morphisms: a combined copula and mass transportation approach to multivariate quantiles.
Our purpose is both conceptual and practical. On the one hand, we discuss the question which properties are basic ingredients of a general conceptual notion of a multivariate quantile. We propose and argue that the objec...
Selected applications of differential equations in Vanilla Options valuation.
In financial models one of the basic assumptions about investors is that they want to gain as much as it is possible but they have aversion taking the risk. Each investing strategy can be considered as a compromise betwe...
Extremal particles in branching processess
The purpose of this study is to investigate two related spatial branchingmodels with the unbounded branching intensity. The objective is to describe theasymptotic behaviour of the extremal particle.
Approximative solutions of optimal stopping and selection problems
In this paper we review a series of developments over the last 15 years in which a general method for the approximative solution of finite discrete time optimal stopping and choice problems has been developed. This metho...
On graduation of enrolment size in a multi-echelon educational system
This paper focuses on an educational system wherein demotion and double promotion are not allowed. The total enrolment in such a system is modelled as a linear model within the context of factor analysis. The goal is to...