## First-Degree Stochastic Dominance

First-Degree Stochastic dominance: It is a form of stochastic ordering that means ordering something that is random. In decision theory and decision analysis this concept allow to rank different probability distribution over possible outcomes. Stochastic dominance allow to determine the preference of an expected utility maximizer between different probability distributions over possible outcomes, with minimal knowledge about the decision maker's utility function.

Set W the decision maker's wealth level and U his utility function. Assume that U is weakly increasing and that more is preferred to less. Designate F and G generic cumulative distribution functions of result of different choices. F first order stochastically dominates G if and only if:

so F is strictly preferred to G. *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