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中文摘要：
AS指标是诺贝尔经济学奖得主Aumann与其合作者Serrano近期基于不确定条件下的选择理论提出的新的风险度量指标,具有诸多优点,被学者们广泛关注.本文基于均值-AS模型研究了正态分布和一般分布下的资产配置问题.在正态分布下,得到了组合边界的解析式,深入探讨了组合边界的特征.在一般分布下,将AS指标的矩估计式嵌入均值-AS模型,实现了风险估计与投资组合优化同步进行.在较弱的条件下,证明了均值-AS模型是凸优化问题,可基于迭代思想设计算法得到模型的数值解.蒙特卡洛模拟结果表明该模型和算法准确有效.最后,基于中国A股市场数据给出了实例分析.
英文摘要：
The AS index is a new risk measure put forward recently by Aumann and Serrano who are inspiredby the theory of choice under uncertainty. It has many advantages over other risk measures andattracts many scholars. In this paper,we consider an asset allocation problem with the Mean-AS model under normal distribution and general distribution assumption,respectively. In the former case,we obtain an analytical expression of portfolio frontier and thoroughly discuss the characteristics of portfolio frontier. In the latter case,we embody the AS moment estimator into the Mean-AS portfolio optimization model and implement risk estimation and portfolio optimization simultaneously. Under very mild conditions,we prove that the Mean-AS model is a convex optimization problem and an iterative algorithm can be designed to obtain its numerical solution. Monte Carlo simulation results show that the Mean-AS model and our algorithm are accurate and effective. Finally,an empirical case of stock portfolio in Chinese A-stock market is illustrated.
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