Samuelson's Fallacy of Large Numbers and Optional Stopping

8 Pages Posted: 21 Jan 2003

See all articles by Erol A. Pekoz

Erol A. Pekoz

Boston University - Department of Operations and Technology Management

Abstract

Accepting a sequence of independent positive mean bets that are individually unacceptable is what Samuelson called a fallacy of large numbers. Recently, utility functions were characterized where this occurs rationally, and examples were given of utility functions where any finite number of good bets should never be accepted. Here the author shows how things change if you are allowed the option to quit early: Subject to some mild conditions, you should essentially always accept a sufficiently long finite sequence of good bets. Interestingly, the strategy of quitting when you get ahead does not perform well, but quitting when you get behind does. This sheds some light on more possible behavioral reasons for Samuelson's fallacy, as well as strategies for handling a series of sequentially observed good investments.

Suggested Citation

Pekoz, Erol A., Samuelson's Fallacy of Large Numbers and Optional Stopping. Available at SSRN: https://ssrn.com/abstract=312744

Erol A. Pekoz (Contact Author)

Boston University - Department of Operations and Technology Management ( email )

United States
617-353-2676 (Phone)

HOME PAGE: http://people.bu.edu/pekoz

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