A Model-Free Continuum of Degrees of Risk Aversion

44 Pages Posted: 30 Jan 2017 Last revised: 1 Apr 2020

See all articles by Tiantian Mao

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: February 19, 2017

Abstract

We establish a theory for a continuum of degrees of risk aversion and risk seeking, referred to as fractional risk aversion and risk seeking. The proposed degrees are well defined for any distribution-based monotone preference on any set of prospects; no particular model assumption is required on the preference. The two degrees combined together intuitively reflect a decision-maker's attitude towards risk. We characterize fractional risk aversion and risk seeking in the models of rank-dependent utility (RDU) and cumulative prospect theory (CPT) for four different classes of sets of prospects. For instance, the degree of risk aversion for an RDU preference is equal to the ratio between its index of pessimism and its index of greediness; both indices depend on the set of prospects at consideration.

Keywords: risk aversion, risk seeking, stochastic dominance, expected utility, rank-dependent utility, cumulative prospect theory

Suggested Citation

Mao, Tiantian and Wang, Ruodu, A Model-Free Continuum of Degrees of Risk Aversion (February 19, 2017). Available at SSRN: https://ssrn.com/abstract=2907499 or http://dx.doi.org/10.2139/ssrn.2907499

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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