Before revision:  These stochastic orders allow us to compare two lotteries, where one lottery has a higher expected value and is also riskier than the other lottery. The main motivation for introducing the \alpha,[a,b] -convex decreasing stochastic orders is that they allow us to derive novel comparative statics results for important applications in economics that could not be derived using previous stochastic orders.
After revision:  These stochastic orders are generated by a novel set of "very" concave functions where \alpha parameterizes the degree of concavity. The \alpha,[a,b] -convex decreasing stochastic orders is that they allow us to derive novel comparative statics results for important applications in economics that could not be derived using previous stochastic orders.