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中文摘要：
研究了泰勒级数对效用函数的收敛条件,力求能够使得泰勒级数成为效用函数的合理近似,从而保证投资组合优化问题的近似解收敛于真实解,最终实现最大化期望效用的投资组合优化问题得以有效解决。在期望效用最大化的泰勒级数近似模型基础上,以HARA效用函数为背景,得到了收益率相对泰勒级数展开点的偏离程度决定了泰勒级数收敛性质的结论,进而提出了合理选择泰勒级数展开点以保证收敛性的方法,该方法意味着在收益率分布具有正偏度的情况下,以往通行的在收益率数学期望处展开泰勒级数的方法不具有合理性,上述分析结论通过数据分析得到了验证。
英文摘要：
Convergence conditions of Taylor series to expected utility function are studied to guarantee the convergence of approximate solution to real solution.Under the setting of HARA utility,it is deducted that the convergence property of Taylor series is decided with how the rate of return deviates from the expansion point,then the approach is suggested of how to select expansion point reasonably to guarantee the convergence of Taylor series to expected utility function.Based on the suggested approach,when return distribution is positively skewed,the general expansion point,i.e.the expectation of portfolio return,is unreasonable.Finally the suggested approach is verified through numerical examples.
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