Optimal Stopping Policy for Multivariate Sequences a Generalized Best Choice Problem

Two Choice Optimal Stopping∗†

Let Xn, . . . , X1 be i.i.d. random variables with distribution function F . A statistician, knowing F , observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to stop at a value of X as small as possible. Let V 2 n equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We o...

Generalized best choice problem based on the information economics approach

We consider the problem of choosing the ‘best choice’ among a certain number of objects that are presented to a decision-maker in sequential order. Such a sequential selection problem is commonly referred to as the ‘best choice problem’, and its optimal stopping rule has been obtained either via the dynamic programming approach or via the Markovian approach. Based on the theory of information e...

The Problem of Optimal Stopping

The problem of Optimal Stopping is of fundamental importance for sequential analysis, for the detection of signals in a background of noise, and also for pricing American-type options in the modern theory of finance. We shall review in this talk two relatively recent approaches to this problem: the deterministic or “pathwise” approach of Davis & Karatzas (1994), and the “integral representation...

On a simple optimal stopping problem

L.A. Shepp has posed aild analyzed the problem of optimal random drawinp with Jut replacement from an urn containing predetermined numbers of plus and minus balls. ;Here Shepp’s results are extended by improving the bounds on value; of penturbeu urns, deriving an exact algorithm for the urn values and computing the stopping boundary for urns of u-, tn 200 balls.

STUDIES ON THE THEORY OF OPTIMAL STOPPING AND ITS APPLICAT10NS TO BEST CHoICE PROBLEMS

A new strategy for Robbins' problem of optimal stopping

In this article we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest non-trivial examples combining rank dependent rules with threshold rules. This rule attains an expected rank lower than the best upper bounds obtained in the literature so far, in pa...