Some Applications of Stochastic Dominance in Economy

There exists a vast range of applications of Stochastic Dominance (SD) rules in different areas of knowledge, such as: Mathematics, Statistic, Biology, Sociology, Economy, etc. Currently, the main areas of application of SD in Economics and Finance are: efficient portfolio selection, asset valuation, risk, insurance, etc. In this talk we will show the utility of SD in Economics.For that, we will start by explaining the classic concepts of SD and their economic interpretation, as well as other definitions used in this context (likelihood ratio order, hazard rate order, Lorenz’s order level crossing order, etc). One of the main topics we will treat is optimal portfolio selection and its relation with associated weighted random variables and utility functions. In particular, we will establish relations between the utilities of the weighted random variables, given the stochastic relations of the original random variables from which we obtained the weighted random variables. Another context in which SD rules are applied is the ruin and risk problems; we will show a generalization of the classic ruin mode and some SD relations between ruin times of two (stochastic) risk processes. Also SD rules can be used in asset valuation context; we will treat, as an example, the Cox and Rubinstein’s model. Others applications of SD rules will also be commented, including: Black Scholes’ model, integral stochastic calculus, inventory theory, chains, etc.