Samuelson's Fallacy of Large Numbers With Decreasing Absolute Risk Aversion

Whelan, Karl (2024): Samuelson's Fallacy of Large Numbers With Decreasing Absolute Risk Aversion.

Abstract

Samuelson (1963) conjectured that accepting multiple independent gambles you would reject on a stand-alone basis violated expected utility theory. Ross (1999) and others presented examples where expected utility maximizers would accept multiple gambles that would be rejected on a stand-alone basis once the number of gambles gets large enough. We show that a stronger result than Samuelson's conjecture applies for DARA preferences over wealth. Expected utility maximizers with DARA preferences have threshold levels of wealth such that those above the threshold will accept N positive expected value gambles while those below will not and these thresholds are increasing with N.

• Item Type: MPRA Paper
• Language: English
• Keywords: Risk aversion; Paul Samuelson; Law of large numbers
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

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