效用最大化、风险厌恶与随机优势
Utility Maximization, Risk Aversion, and Stochastic Dominance
摘要：
考虑一个投资者动态交易，以最大化终端财富的期望效用。我们的目的是研究她的风险厌恶和最优终端收益分布之间的依赖关系。经济学的直觉告诉我们，高风险厌恶会导致一个相当集中的分布，而低风险厌恶会导致更高的平均回报，代价是更广泛的分布。Dybvig和Wang [J. Econ. Theory，2011，即将出现]发现，这个想法确实可以转化为单期模型中严格的数学陈述。更具体地说，他们表明，较低的风险厌恶导致的回报是更大的二阶随机优势。在本研究中，我们将他们的结果推广到（弱）完全连续时间模型。我们还补充了一个特设的反例Dybvig和王，通过显示这些结果是“脆弱的”，在这个意义上说，他们失败的基本上任何模型，如果后者是扰动的一组任意小的概率。另一方面，我们建立，他们举行的权力投资者的模型（条件）独立增量。
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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