Abstract
AbstractAlmost stochastic dominance is a relaxation of stochastic dominance, which allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. The authors first discuss the relations between almost first-degree stochastic dominance (AFSD) and the second-degree stochastic dominance (SSD), and demonstrate that the AFSD criterion is helpful to narrow down the SSD efficient set. Since the existing AFSD criterion is not convenient to rank transformations of random variables due to its relying heavily on cumulative distribution functions, the authors propose the AFSD criterion for transformations of random variables by means of transformation functions and the probability function of the original random variable. Moreover, they employ this method to analyze the transformations resulting from insurance and option strategy.
Highlights
Modelling the portfolio selection criteria of rational decision makers represents a central problem in the area of finance and economic
In consideration of the characteristic of this problem, we develop a new form of almost first-degree stochastic dominance (AFSD), which is expressed by the transformation functions and the probability function of the original random variable
Due to the enormous controversy over the definitions of the second-degree and higher-degree almost stochastic dominance, and more significantly, they cannot be directly extended to the transformations case, this paper will only focus on the AFSD criterion for transformations of random variables
Summary
Modelling the portfolio selection criteria of rational decision makers represents a central problem in the area of finance and economic. Leshno and Levy (2002) suggest that the stochastic dominance rules are unable to reveal such preferences because they account for extreme utility functions, which rarely represent preferences of investors in practice. They introduce the concept of almost stochastic dominance (ASD), which only considers preferences under non-extreme utility functions. It is generally known that economic and financial activities usually induce transformations of an initial risk, which results in a new type of problem of how to rank transformations of random variables In this case, the choice criteria of ASD, based on the cumulative distribution functions, are inconvenient to distinguish transformations of random variables.
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