Prudence with Multiplicative Risk

In this paper we analyze the conditions under which the presence of a multiplicative background risk induces a more “prudent” behavior.

Author(s):

Octave Jokung-Nguena

Professor, EDHEC Business School

We show that the results from Kimball (1990) concerning the convexity of the marginal utility are no longer sufficient with multiplicative risk. An agent is multiplicative risk prudent when the coefficient of relative prudence is greater than two. We introduce the concept of quintessence in order to guarantee the decrease of relative temperance. Both decreasing relative prudence and decreasing relative temperance are sufficient to guarantee more prudent behavior with a multiplicative risk-prudent agent. Nevertheless, the convexity of the relative prudence combined with the decrease (respectively increase) of the relative prudence implies more prudent behavior when the agent is multiplicative risk prudent (respectively risk imprudent). Surprisingly, the derived utility function inherits some properties of the direct utility function and the presence of the multiplicative background risk preserves comparative riskprudent behavior under certain conditions. Our results apply to savings and portfolio selection. For example, a risk-prudent agent will lower his or her willingness to hold risky assets when he or she faces a multiplicative background risk if his or her relative risk aversion is convex and decreases.

Type: Working paper
Date: le 01/12/2008
Research Cluster : Finance

See Also

EDHEC official partner of VIVATECHNOLOGY 2022: 400 tickets offered!
News
- 20-05-2022
EDHEC is once again a partner of the unmissable tech event of the year, Viva Technology...
EDHEC partners with VIVATECH 2022 and offers 400 tickets to EDHEC students
News
- 20-05-2022
EDHEC is once again a partner of the unmissable tech event of the year, Viva Technology...
(Invitation) Inauguration of the Management in Innovative Health Chair - May 30, 2022 in Paris
News
- 17-05-2022
Emmanuel Métais, Dean of EDHEC Business School and Christophe Durand, General Manager...
News
- 10-05-2022
Live on YouTube !