Jensen's Inequality, Parameter Uncertainty, and Multi-period Investment
研究发现，当决策依赖未知参数的凸或凹函数时，统计估计误差调整的方向与决策需求相反。以多期投资为例，詹森不等式的正确应用颠覆了传统金融直觉：负风险溢价的投资可能盈利，风险厌恶者可能无限需求风险资产，甚至不分散投资。
Classical approaches to estimation and decisions requiring estimation often are at odds. When values critical to the decision are convex or concave functions of unknown parameters, the statistician's estimation error adjustments are the opposite of what is appropriate for the decision. We illustrate the conflict by studying multi-period investment problems. The proper application of Jensen's inequality to the decision turns finance intuition on its head: Multi-period investments with negative risk premia can be profitable, risk-averse investors can have infinite demand for risky securities, settings exist in which risk-averse investors should not diversify, and demand for mutual funds with negative alphas may be rational.