In this paper we provide a novel family of stochastic orders that generalizes second order stochastic dominance, which we call the $\alpha ,[a,b]$-concave stochastic orders. These stochastic orders are generated by a novel set of “very” concave functions where $\alpha$ parameterizes the degree of concavity. The $\alpha ,[a,b]$-concave stochastic orders allow us to derive novel comparative statics results for important applications in economics that cannot be derived using previous stochastic orders. In particular, our comparative statics results are useful when an increase in a lottery’s riskiness changes the agent’s optimal action in the opposite direction to an increase in the lottery’s expected value. For this kind of situation, we provide a tool to determine which of these two forces dominates — riskiness or expected value. We apply our results in consumption–savings problems, self-protection problems, and in a Bayesian game.

在本文中，我们提供了一个新的随机阶系列，它概括了二阶随机优势，我们称之为 $\alpha ,[\mathrm{一种},乙]$- 凹随机订单。这些随机订单是由一组新的“非常”凹函数生成的，其中$\alpha$参数化凹度。这$\alpha ,[\mathrm{一种},乙]$-凹随机顺序使我们能够为经济学中的重要应用得出新颖的比较静态结果，而这些结果无法使用以前的随机顺序得出。特别是，当彩票风险的增加使代理的最佳行动与彩票预期值的增加相反时，我们的比较静态结果很有用。对于这种情况，我们提供了一种工具来确定这两种力量中的哪一种占主导地位——风险性或预期价值。我们将我们的结果应用于消费储蓄问题、自我保护问题和贝叶斯游戏。