On Estimating the Expected Rate of Return in Diffusion Price Models with Application to Estimating the Expected Return on the Market
推导并数值模拟了几种重要扩散价格模型中漂移的最大似然估计量，比较其与几何均值、算术均值等标准估计量的时间序列收敛性质，量化了估计预期收益率所需的时间长度。
This paper derives and numerically simulates maximum likelihood estimators for the drift in several important diffusion price models. The time series convergence properties of these estimators are compared to those of standard estimators including the geometric and arithmetic means. Merton (1980) demonstrated that it is difficult to efficiently estimate the drift in a log-normal diffusion model. We qualify and strengthen his result by noting that his estimator is the maximum likelihood estimator and by applying our simulation results. However, we also demonstrate that it is possible to efficiently estimate the drift in other useful diffusion price models. In particular, by asking just how much time is needed in order for the maximum likelihood estimators of the drift in different diffusion processes to converge, these results qualify and quantify Black's (1993) statement that “we need such a long period to estimate the average that we have little hope of seeing changes in expected return."