论文标题
小/大金融市场的指数效用最大化
Exponential utility maximization in small/large financial markets
论文作者
论文摘要
当返回向量遵循比普通分布更一般的分布时，以封闭形式获得最大化最佳投资组合是一个艰巨的问题。在本说明中，我们在基于有限的许多资产的市场中给出了封闭的表达式，以使最佳投资组合在返回矢量遵循正常的均值变化混合模型时最大化预期的指数实用程序。然后，我们还基于正常的均值变化混合模型来考虑大型金融市场，并表明，在指数实用程序下，基于小市场的最佳公用事业公司汇聚到大型金融市场的最佳实用性。该结果尤其表明，要达到最佳公用事业级别的投资者需要将其投资组合多样化，以将无限的许多资产包括在其投资组合中，并且基于任何仅有限的许多资产的投资组合，他们永远无法达到最佳的公用事业水平。在本文中，我们还考虑了更通用的实用程序功能的投资组合优化问题，并提供了一个易于实现的数值程序来定位最佳投资组合。尤其是，我们在本文的这一部分中的方法减少了将最佳投资组合定位为一般效用函数类别的三维问题的高维问题。
Obtaining utility maximizing optimal portfolios in closed form is a challenging issue when the return vector follows a more general distribution than the normal one. In this note, we give closed form expressions, in markets based on finitely many assets, for optimal portfolios that maximize the expected exponential utility when the return vector follows normal mean-variance mixture models. We then consider large financial markets based on normal mean-variance mixture models also and show that, under exponential utility, the optimal utilities based on small markets converge to the optimal utility in the large financial market. This result shows, in particular, that to reach optimal utility level investors need to diversify their portfolios to include infinitely many assets into their portfolio and with portfolios based on any set of only finitely many assets, they never be able to reach optimum level of utility. In this paper, we also consider portfolio optimization problems with more general class of utility functions and provide an easy-to-implement numerical procedure for locating optimal portfolios. Especially, our approach in this part of the paper reduces a high dimensional problem in locating optimal portfolio into a three dimensional problem for a general class of utility functions.
