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

The FIR-PRI Awards “Finance & Sustainability” prize for “best pedagogical innovation”: preparing future generations to fight climate change.
News
- 18-10-2021
At EDHEC, we want to take part in the fight against climate change. Through our...
Stanford Summer Program: one of EDHEC’s opportunities to grab
News
- 14-10-2021
Shantanu Khandelwal, Master 2 student had the opportunity to join the selective...
Immersion at Station F for start-up challenge finalists !
News
- 13-10-2021
Devised for students with start-up projects on the Pre-Master and Master 1 years of the...
Financing your MBA - are you eligible for a scholarship?
News
- 12-10-2021
How to finance your Global MBA abroad is a critical question you need to think about...