效用最大化、风险规避与随机支配

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摘要翻译：
考虑一个投资者动态交易，以最大化终端财富的预期效用。我们的目的是研究她的风险厌恶与最优最终收益分布之间的依赖关系。经济直觉表明，高风险厌恶导致相当集中的分布，而较低的风险厌恶导致较高的平均收益，以牺牲更广泛的分布为代价。Dybvig和Wang[J.Econ.Theory,2011,to出现]发现这个想法确实可以在单周期模型中变成一个严格的数学陈述。更具体地说，它们表明，较低的风险厌恶导致的收益在二阶随机优势方面较大。在本研究中，我们将它们的结果推广到（弱）完全连续时间模型。我们还补充了Dybvig和Wang的一个特别的反例，表明这些结果是“脆弱的”，因为它们基本上在任何模型中都失败，如果后者在任意小概率的集合上被扰动的话。另一方面，我们在具有（条件）独立增量的模型中建立了它们对电力投资者的成立。
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英文标题：
《Utility Maximization, Risk Aversion, and Stochastic Dominance》
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作者：
Mathias Beiglboeck, Johannes Muhle-Karbe, Johannes Temme
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最新提交年份：
2011
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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英文摘要：
  Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff.   Economic intuition suggests that high risk aversion leads to a rather concentrated distribution, whereas lower risk aversion results in a higher average payoff at the expense of a more widespread distribution.   Dybvig and Wang [J. Econ. Theory, 2011, to appear] find that this idea can indeed be turned into a rigorous mathematical statement in one-period models. More specifically, they show that lower risk aversion leads to a payoff which is larger in terms of second order stochastic dominance.   In the present study, we extend their results to (weakly) complete continuous-time models. We also complement an ad-hoc counterexample of Dybvig and Wang, by showing that these results are "fragile", in the sense that they fail in essentially any model, if the latter is perturbed on a set of arbitrarily small probability. On the other hand, we establish that they hold for power investors in models with (conditionally) independent increments.
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PDF链接：
https://arxiv.org/pdf/1104.0761

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关键词：效用最大化 风险规避 最大化 Quantitative distribution lower study terminal 交易 risk