A Critical Comparison of Three Notions of Fractional Stochastic Dominance

40 Pages Posted: 5 Sep 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: July 3, 2020

Abstract

Two notions of fractional stochastic dominance are recently proposed by Muller et al. (2017) and Huang et al. (2020), respectively. Our main objective is to understand the comparative advantages of the two notions, as well as their suitability in different contexts, by establishing several new technical results. For a more comprehensive comparison, we further include a third natural notion of fractional stochastic dominance based on the coefficient of relative risk aversion. Among the three notions, it turns out that one can be seen as a logarithmic version of second-order stochastic dominance (SSD), another one can be seen as a power version of SSD, whereas there does not exist a transformation to associate the last one with SSD. We find that these notions of fractional stochastic dominance are naturally connected to five classes of risk measures, including Value-at-Risk, Expected Shortfall, expectiles, entropic risk measures, and loss certainty equivalents. The three notions are further characterized in the contexts of the rank-dependent utility model and the cumulative prospect theory. We make some recommendations on which notion to use in specific situations, as they all have their own merits.

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

Suggested Citation

Mao, Tiantian and Wang, Ruodu, A Critical Comparison of Three Notions of Fractional Stochastic Dominance (July 3, 2020). Available at SSRN: https://ssrn.com/abstract=3642983

Tiantian Mao (Contact Author)

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

96, Jinzhai Road
Hefei, Anhui 230026
China

Ruodu Wang

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

Waterloo, Ontario N2L 3G1
Canada

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