Static Mean-Variance Analysis with Uncertain Time Horizon
将马科维茨均值方差分析推广到退出时间不确定的情形，发现标准有效组合可能不再有效，忽视时间不确定性会导致显著的效率损失。
We generalize Markowitz analysis to the situations involving an uncertain exit time. Our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return. However, inputs are now given by the generalized expressions for mean and variance-covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns. Although efficient frontiers in the generalized and the standard Markowitz case may coincide under certain conditions, we demonstrate that, by means of an example, in general that is not true. In particular, portfolios efficient in the standard Markowitz sense can be inefficient in the generalized sense and vice versa. As a result, an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions. Numerical simulations show that a significant efficiency loss can be induced by an improper use of standard mean-variance analysis when time horizon is uncertain.