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A bold strategy is not always optimal in the presence of inflation

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Robert W. Chen ,
Larry A. Shepp  and
Alan Zame
Robert W. Chen*
Affiliation:
University of Miami
Larry A. Shepp*
Affiliation:
Rutgers University
Alan Zame*
Affiliation:
University of Miami
*
∗ Postal address: Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA.
∗∗∗ Postal address: Department of Statistics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA.
∗ Postal address: Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA.
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Abstract

A gambler, with an initial fortune less than 1, wants to buy a house which sells today for 1. Due to inflation, the price of the house tomorrow will be 1 + α, where α is a nonnegative constant, and will continue to go up at this rate, becoming (1 + α) n on the nth day. Once each day, he can stake any amount of fortune in his possession, but no more than he possesses, on a primitive casino. It is well known that, in a subfair primitive casino without the presence of inflation, the gambler should play boldly. The presence of inflation would motivate the gambler to recognize the time value of his fortune and to try to reach his goal as quickly as possible; intuitively, we would conjecture that the gambler should again play boldly. However, in this note we will show that, unexpectedly, bold play is not necessarily optimal.

Keywords

Gambling problemprimitive casinooptimal strategybold strategy

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60K99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 587 - 592
Copyright
Copyright © Applied Probability Trust 2004 

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