Modeling Non-Monotone Risk Aversion Using SAHARA Utility Functions

25 Pages Posted: 15 Feb 2010 Last revised: 8 Sep 2011

See all articles by An Chen

An Chen

Ulm University - Institute of Insurance Science

Antoon Pelsser

Maastricht University; Netspar

Michel Vellekoop

University of Twente - Department of Applied Mathematics

Multiple version iconThere are 2 versions of this paper

Date Written: May 2, 2011

Abstract

We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk-averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases.

We investigate the optimal investment problem under SAHARA utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how SAHARA utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.

Keywords: SAHARA utility, optimal investment problem, dual approach, utility indifference pricing

JEL Classification: G11, G13, G22, D52, C61

Suggested Citation

Chen, An and Pelsser, Antoon A. J. and Vellekoop, Michel, Modeling Non-Monotone Risk Aversion Using SAHARA Utility Functions (May 2, 2011). Journal of Economic Theory, Vol 146, 2011, Available at SSRN: https://ssrn.com/abstract=1552079

An Chen

Ulm University - Institute of Insurance Science ( email )

Ulm, 89081
Germany

HOME PAGE: http://www.uni-ulm.de/mawi/ivw/team

Antoon A. J. Pelsser (Contact Author)

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Michel Vellekoop

University of Twente - Department of Applied Mathematics ( email )

P.O. Box 217
7500 AE Enschede
Netherlands

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