Multiplicative Risk Prudence

Abstract

We examine the optimal saving decision of individuals who face a multiplicative risk. An individual is defined to be multiplicative risk prudent if multiplying a pure risk to her future wealth raises her optimal savings. We show that an individual is multiplicative risk prudent if and only if her relative risk prudence uniformly exceeds two. Our result suggests a more restrictive assumption that needs to be imposed on preferences for individuals to be risk prudent.

Keywords: Multiplicative risk, Risk prudence, Precautionary saving

JEL Classification: E21, D81