Background risk and small-stakes risk aversion

TL;DR

This paper demonstrates that common theories of decision-making under risk cannot simultaneously satisfy risk aversion over small gambles, respect for stochastic dominance, and consideration of background risk under plausible conditions.

Contribution

It identifies fundamental limitations of existing risk theories when background risk is present, highlighting the need for revised models.

Findings

No standard theory satisfies all three postulates simultaneously

Background risk influences risk aversion and decision consistency

Theoretical incompatibility under plausible assumptions

Abstract

We show that under plausible levels of background risk, no theory of choice under risk -- such as expected utility theory, prospect theory, or rank dependent utility -- can simultaneously satisfy the following three economic postulates: (i) Decision makers are risk-averse over small gambles, (ii) they respect stochastic dominance, and (iii) they account for background risk.