What Is Stochastic Dominance?

Stochastic dominance provides a simple tool for risk asset selection (Whitmore and Findlay, 1978). We explain the stochastic dominance relationship with a simple example: Suppose an investor wants to choose between two risky assets X and Y. If the return of X always exceeds the return of Y in any future situation, as long as the investor is It will never be satisfied, then the investor will not hold Y, because the return from holding X will be better.

Random advantage

Right!

Stochastic dominance is

Using this method, there is no need for the utility function of investors,

There are three main types of stochastic dominance relationships: first-order stochastic dominance (FSD); second-order stochastic dominance (SSD) and third-order stochastic dominance (TSD). The strict definition of stochastic dominance is: Assuming the cumulative distribution functions (CDF) of the returns of X and Y are F1 and G1, respectively, X is a first-order stochastic dominance over Y if and only if

A first-order random account is better than B-from the perspective of all individuals with more preferences and less aversion, A is better than B;

A second-order stochastic is better than B-from the perspective of all risk-averse individuals, A is better than B;

A second-order monotonic random account is better than B-from all individuals who have more preferences but less aversion and risk aversion, A is better than B;

A's third-order stochastic account is better than B-from the perspective of all individuals who have more preference but less aversion, risk aversion, and decreasing absolute risk aversion, A is better than B.

Cumulative outlook theory

Level-dependent utility theory

Outlook theory