## Second-Degree Stochastic dominance

It is a form of stochastic ordering that means to order random result distribution. It is useful when first-degree stochastic dominance not reach to give us the best choice from two random alternatives.

We have to assume that the agent is risk adverse and thus have a utility function of economic return, positive but decreasing slope. In the way of second-degree stochastic dominance, A is preferred to B if the following formula is true for all values of the variable x and with at least one strong inequality:

So frequency distributions of outcomes of alternatives are compared based on areas under their cumulative distribution functions. Second-degree stochastic dominance requires that the curve of dominant cumulative distribution function that is the best choice, lies everywhere below and to the right of others alternatives.

*Bibliography Hardaker *

J. B., Huirne R. B. M.,Coping with risk in Agriculture, CABI, 2004

MIT OpenCourseWare, Microeconomic Theory III, Spring 2010

Editor: Giuliano DI TOMMASO