Stochastic dominance and mean–variance measures of profit and loss for business planning and investment

In this paper, we first extend the stochastic dominance (SD) theory by introducing the first three orders of both ascending SD (ASD) and descending SD (DSD) to decisions in business planning and investment to risk-averse and risk-loving decision makers so that they can compare both return and loss. We provide investors with more tools for empirical analysis, with which they can identify the first-order ASD and DSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors and business planners to identify the third order ASD and DSD prospects and make better choices.To complement the stochastic dominance approach, we also introduce an improved mean–variance criterion to decisions in business planning or investment on both return and loss for risk-averse and risk-loving investors. We then illustrate the superiority of the present approaches with well-known examples in the literature and discuss the relationship between the improved stochastic dominance and mean–variance criteria.