Optimal derivatives: portfolios, payoffs and preferences
本文扩展了增长最优衍生品，使其能容纳不同于对数效用的风险偏好，分析了幂效用投资者的行为，并证明在现实概率下的幂投资者可视为在短视概率下的对数投资者，最后用Black-Scholes模型演示了实施方法。
This article presents an extension to the growth optimal derivative that can accommodate risk preferences differing from those of logarithmic utility. Analysis of the optimal derivative provides interesting insights into the behaviour of power investors. We show that power investors under the real-world probability can be viewed as logarithmic investors under the myopic probability of Guasoni and Robertson [(2012). “Portfolios and Risk Premia for the Long Run.” Annals of Applied Probability, 22 (1), 239–284]. Furthermore, this intuition provides criteria for establishing whether fractional Kelly betting is optimal for power investors. Finally, the Black–Scholes model is used to demonstrate how the optimal derivative can be implemented and we show that our approach is consistent with classical techniques.