## The Annals of Mathematical Statistics

### On the Dubins and Savage Characterization of Optimal Strategies

William D. Sudderth

#### Abstract

An elegant characterization of optimal strategies for gambling problems was given by Dubins and Savage in the finitely additive setting of their book How to Gamble If You Must. An exposition of their ideas is given here in a measurable, countably additive framework. With the additional measurability assumptions, it becomes possible to treat a larger class of payoff functions. Also, necessary and sufficient conditions are given for a strategy to be $\epsilon$-optimal, a problem not considered by Dubins and Savage.

#### Article information

Source
Ann. Math. Statist., Volume 43, Number 2 (1972), 498-507.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692630

Digital Object Identifier
doi:10.1214/aoms/1177692630

Mathematical Reviews number (MathSciNet)
MR300333

Zentralblatt MATH identifier
0239.62052

JSTOR