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Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance

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  • Ghossoub, Mario
  • He, Xue Dong

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 firm (the underwriter) plays an insurance role: through the underwriting contract, the issuing firm 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 firm 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.

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  • Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pa:p:6-22
    DOI: 10.1016/j.insmatheco.2020.06.007
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    1. Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.

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    More about this item

    Keywords

    Rank-dependent expected utility; Comparative risk aversion; Risk sharing; Optimal underwriting; Firm-commitment contract;
    All these keywords.

    JEL classification:

    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G52 - Financial Economics - - Household Finance - - - Insurance
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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