## 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