A Minimax Portfolio Selection Rule with Linear Programming Solution
提出一种基于历史收益率数据、以最小化最大损失为风险度量、通过线性规划求解的投资组合选择规则，避免了均值-方差模型的逻辑问题，并支持整数或0-1约束。
A new principle for choosing portfolios based on historical returns data is introduced; the optimal portfolio based on this principle is the solution to a simple linear programming problem. This principle uses minimum return rather than variance as a measure of risk. In particular, the portfolio is chosen that minimizes the maximum loss over all past observation periods, for a given level of return. This objective function avoids the logical problems of a quadratic (nonmonotone) utility function implied by mean-variance portfolio selection rules. The resulting minimax portfolios are diversified; for normal returns data, the portfolios are nearly equivalent to those chosen by a mean-variance rule. Framing the portfolio selection process as a linear optimization problem also makes it feasible to constrain certain decision variables to be integer, or 0-1, valued; this feature facilitates the use of more complex decision-making models, including models with fixed transaction charges and models with Boolean-type constraints on allocations.