英文标题：
《Convergence of Optimal Expected Utility for a Sequence of Discrete-Time
Markets》
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作者：
David M. Kreps, Walter Schachermayer
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最新提交年份：
2020
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英文摘要：
We examine Kreps\' (2019) conjecture that optimal expected utility in the classic Black--Scholes--Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that \"approach\" the BSM economy in a natural sense: The $n$th discrete-time economy is generated by a scaled $n$-step random walk, based on an unscaled random variable $\\zeta$ with mean zero, variance one, and bounded support. We confirm Kreps\' conjecture if the consumer\'s utility function $U$ has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function $U$ with asymptotic elasticity equal to 1, for $\\zeta$ such that $E[\\zeta^3] > 0.$
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中文摘要：
我们检验了Kreps（2019）的猜想，即经典的Black-Scholes-Merton（BSM）经济中的最优预期效用是一系列离散时间经济体的最优预期效用的极限，这些离散时间经济体在自然意义上“接近”BSM经济体：第n美元离散时间经济体是由一个按比例的n美元步随机游走产生的，该游走基于平均值为零的无标度随机变量$\\ zeta$，方差1和有界支撑。如果消费者的效用函数$U$的渐近弹性严格小于1，我们证实了Kreps的猜想，并且我们提供了一个反例，证明了效用函数$U$的渐近弹性等于1，对于$zeta$，使得$E[\\zeta^3]>0$
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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