## The Annals of Statistics

### A Note on the Characterization of Optimal Return Functions and Optimal Strategies for Gambling Problems

R. van Dawen

#### Abstract

We consider finite state gambling problems with the Dubins and Savage payoff and with the $\lim\inf$ payoff. For these models we show that the optimal return function with respect to all stationary strategies can be characterized similarly to the optimal return function. This enables us then to characterize those stationary strategies which are optimal within the set of all stationary strategies in the same way as it was done for optimal strategies by Dubins and Savage.

#### Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 832-835.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176349563

Digital Object Identifier
doi:10.1214/aos/1176349563

Mathematical Reviews number (MathSciNet)
MR790581

Zentralblatt MATH identifier
0573.93054

JSTOR