Comparative Risk Aversion in RDEU with Applications to Optimal Underwriting of Securities Issuance

51 Pages Posted: 19 Jan 2018 Last revised: 9 Jun 2020

See all articles by Mario Ghossoub

Mario Ghossoub

University of Waterloo

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Date Written: December 20, 2019

Abstract

We provide a characterization of comparative weak risk aversion and comparative RDEU risk aversion for RDEU preferences and, in particular, we correct a claim made by Quiggin (1993) regarding comparative RDEU risk aversion. We then apply the analysis of comparative risk aversion to a problem of optimal design of underwriting contracts in securities issuance. Specifically, in public offerings of equity, an investment banking rm (the underwriter) plays an insurance role: through the underwriting contract, the issuing rm transfers the issue risk to the underwriter, as would an insured to an insurer. We extend a classical model proposed by Mandelker and Raviv (1977) to situations where the issuing rm and the underwriter have RDEU preferences. Assuming that the issuing company's and the underwriter's utility functions are concave and linear, respectively, and that either the underwriter is risk neutral or both the issuing company and underwriter are strongly risk averse, we show that a firm-commitment contract is optimal if and only if the issuing company's probability weighting function dominates the underwriter's.

Keywords: Rank-dependent expected utility, comparative risk aversion, risk sharing, optimal underwriting, firm-commitment contract

JEL Classification: G24, G52, D89

Suggested Citation

Ghossoub, Mario and He, Xue Dong, Comparative Risk Aversion in RDEU with Applications to Optimal Underwriting of Securities Issuance (December 20, 2019). Insurance: Mathematics and Economics, Forthcoming., Available at SSRN: https://ssrn.com/abstract=3101176 or http://dx.doi.org/10.2139/ssrn.3101176

Mario Ghossoub (Contact Author)

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1
Canada

HOME PAGE: http://uwaterloo.ca/scholar/mghossou

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

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