A Note on Optimal Estimation from a Risk-Management Perspective under Possibly Misspecified Tail Behavior
研究在资产收益分布尾部可能被错误设定的情况下，如何从风险管理角度选择最优估计方法，以最小化名义VaR与实际VaR的偏差，发现高斯最大拟似然估计（最小二乘类）优于最大似然估计。
Many financial time series show leptokurtic behavior—that is, fat tails. Such tail behavior is important for risk management. In this article I focus on the calculation of Value-at-Risk (VaR) as a downside-risk measure for optimal asset portfolios. Using a framework centered on the Student-t distribution, I explicitly allow for a discrepancy between the fat-tailedness of the true distribution of asset returns and that of the distribution used by the investment manager. As a result, numbers for the overestimation or underestimation of the true VaR of a given portfolio can be computed. These numbers are used to rank several well-known estimation methods for determining the unknown parameters of the distribution of asset returns. Minimizing the absolute (percentage) mismatch between the nominal and actual or true VaR leads to the choice of a Gaussian maximum quasilikelihood estimator—that is, a least squares type of estimator. The maximum likelihood estimator has less satisfactory behavior. Outlier-robust es...