Abstract: Mean-variance models for portfolio selection are established by describing security returns as birandom variables. The mathematical expectation and variance of birandom variable are studied. The general computational expressions of mathematical expectation and variance of birandom variable are given. Thus the proposed models can be changed into their crisp equivalent ones when the security returns are chosen as some special birandom variables. The convexity of the models is discussed. The existence and uniqueness of the solutions to the models are verified. The feasibility of the methods is illustrated by an example.

Key words: birandom variable, portfolio selection model, variance of birandom variable, deterministic equivalence

摘要： 将收益率刻画为双随机变量，建立了均值-方差证券投资组合模型；研究并给出了双随机变量期望值和方差的一般计算方法，将模型转化为其确定等价形式；讨论了模型的凸性，证明了模型解的存在性和惟一性；通过数值例子验证了模型和方法的可行性。

关键词: 双随机变量, 投资组合模型, 双随机变量的方差, 确定等价类