统计与管理学院2015年学术报告第16期
【主 题】 Markowitz's Mean-Variance Portfolio Selection Model with Pure Risk
【报告人】 Zuoquan Xu 博士
The Hong Kong Polytechnic University
【时 间】 2015年4月29日（星期三）16:00－17:00
【地 点】 上海财经大学统计与管理学院大楼1208室
【语 言】 英文
【摘 要】 This paper studies a continuous-time robust Markowitz's mean-variance model where a pure risk is involved in the final decision and all the market coefficients are random. The term ``pure risk'' refers to random outcomes about which the only things we know are their moments and/or distributions. Before their occurrence, they are unpredictable, unhedgeable, and uncontrollable. Gains from lottery tickets and payments on insurance contracts are outstanding examples of pure risks. In the model, the target of the investor is set to minimize the variance in the worst scenario over all possible pure risks that could happen. Due to the time-inconsistent feature of the problem, the classical dynamic programming and stochastic control approaches cannot be directly applied to solve the problem. Instead, the quantile optimization method is adopted to tackle the problem. The optimal solution is given in a closed form. It turns out that the mean-variance frontier is neither two half-lines nor a parabola when a pure risk is involved in the decision. This also means that the one-fund and two-fund theorems are invalid, and our model is essentially different from the classical one.
