摘要翻译：
本文给出了一个新的推广二阶随机优势的随机序族，我们称之为$α,[a,b]$-凹随机序。这些随机顺序是由一组新颖的“非常”凹函数产生的，其中$\alpha$参数化凹度。α，[a,b]$-凹随机序允许我们为经济学中的重要应用导出新的比较静力学结果，而这些结果是用以前的随机序无法导出的。特别是，当彩票风险的增加使代理人的最优行为与彩票期望值的增加相反时，我们的比较静力学结果是有用的。对于这种情况，我们提供了一个工具来确定这两种力量中哪一种占主导地位--风险或期望值。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博弈中。
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英文标题：
《The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected Value》
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作者：
Bar Light and Andres Perlroth
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最新提交年份：
2021
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/1908.06398