It is possible in a stock exchange that some candidate securities possess sufficient transaction data, and some others are newly listed and lack enough data. If an investor wants to choose a portfolio that contains two types of securities mentioned, none of the probability theory and uncertainty theory, alone, can be applied. In this case, the chance theory can be useful. For this purpose, in this paper, we discuss the uncertain random portfolio- which is a portfolio contains some candidate securities that have sufficient transaction data and some newly listed ones with insufficient transaction data- selection problem. Indeed, this paper introduces a new risk criterion and proposes a new type of mean-risk model based on this criterion to find the optimal uncertain random portfolio. And in the end, a numerical example is presented for the sake of illustration.

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