The Portfolio Selection Problem with Random Interval-valued Return Rates

The famous mean-variance portfolio selection model introduced by Markowitz in [7] is an important breakthrough in mathematical finance, which deals with uncertainties appearing in financial markets. In real financial market, there may exist two kinds of uncertainties. One is randomness and the other is impreciseness or vagueness. In this paper we study the portfolio selection problem combining randomness with impreciseness by considering asset return rates and risks as random intervals and propose two models. For these models it is important to give a suitable ordering for intervals. Here we use γ-index and satisfactory crisp equivalent system to do it given by Sengupta et al. in [11]. As an application of our models, a numerical example is given whose data comes from a real stock market.