## The Annals of Probability

- Ann. Probab.
- Volume 12, Number 3 (1984), 882-889.

### A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options

#### Abstract

This article tries to unify best choice problems under total ignorance of both the candidates, quality distribution and the distribution of the number of candidates. The result is what we shall call the $e^{-1}$-law because of the multiple role which is played by $e^{-1}$, and this in a more general context as only in the solution of the classical secretary problem. The unification is possible whenever best choice problems can be redefined as continuous time decision problems on conditionally independent arrivals. We shall also give several examples to illustrate how the approach and its implications compare with other models.

#### Article information

**Source**

Ann. Probab. Volume 12, Number 3 (1984), 882-889.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993237

**Digital Object Identifier**

doi:10.1214/aop/1176993237

**Mathematical Reviews number (MathSciNet)**

MR744243

**Zentralblatt MATH identifier**

0553.60047

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

**Keywords**

Best choice problem secretary problem optimal stopping time two person game

#### Citation

Bruss, F. Thomas. A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options. Ann. Probab. 12 (1984), no. 3, 882--889. doi:10.1214/aop/1176993237. https://projecteuclid.org/euclid.aop/1176993237.