Precautionary Effort: Another Trait for Prudence

• Published date: 01 December 2015
• Author: Jingyuan Li,Jianli Wang
• DOI: http://doi.org/10.1111/jori.12054
• Date: 01 December 2015

©2014 The Journal of Risk and Insurance. Vol.82, No. 4, 977–983 (2015).

DOI: 10.1111/jori.12054

Precautionary Effort: Another Trait for Prudence

Jianli Wang

Jingyuan Li

Abstract

This article shows that, in the temporal model of Eeckhoudt, Huang, and

Tzeng (2012), prudence alone is sufficient to obtain a precautionary effort.

Moreover,our conclusions relax the assumption of the convexity of loss prob-

ability. We further analyze the effect of the introduction or deterioration of

background risks on precautionary effort in different settings.

Introduction

The concept of prudence coined by Kimball (1990) has long been related to precaution-

ary savings. Eeckhoudt and Schlesinger (2006) define prudence as a type of preference

over simple lotteries:

Definition 1: (Eeckhoudt and Schlesinger, 2006) An individual is said to be prudent if

the lottery [−k;˜ε]is preferred to the lottery [0; ˜ε−k], where all outcomes of the lotteries have

equal probability, for all initial wealth levels xand for all k>0and all ˜εwith E˜ε=0.

This definition shows that prudence is a type of preference for disaggregation of a

sure loss and a zero-mean random variable. This decision maker (DM) always prefers

to combine bad (˜ε) with good (0) rather than with bad (−k).

Recently, in the framework of intertemporal EU maximization, Crainich, Eeckhoudt,

and Trannoy (2013) show that a risk-seeking and prudent DM chooses a positive pre-

cautionary saving level. They conclude that for risk averters and risk lovers, prudence

guarantees precautionary saving. Thus, we have an economically important behav-

Jianli Wang is at the College of Economics and Management, Nanjing University of

Aeronautics and Astronautics, Nanjing 211106, China. Wang can be contacted via e-mail:

jianliwang2013@gmail.com. Jingyuan Li is at the Department of Finance and Insurance,

Lingnan University, Hong Kong. Li can be contacted via e-mail: jingyuanli@ln.edu.hk. This

work is supported by the Fundamental Research Funds for the Central Universities under

Research Project No. NR2014002, the Faculty Research Grant of Lingnan University under Re-

searchProject No. DR12A9, and Direct Grant for Research of Lingnan University under Research

Project No. DR13C8. The authors would like to thank the coeditor and anonymous referees for

providing valuable suggestions that have led to significant improvement of this article.

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