Portfolio Investment with Options Based on Uncertainty Theory

Abstract

In financial markets, there are situations where investors have the future stock prices according to the experts’ evaluations rather than historical data. Thus, the estimations of the stock prices contain much subjective imprecision instead of randomness. This paper discusses a portfolio investment with options in such a kind of situation. Treating the stock index price as an uncertain variable, we build an uncertain mean-chance portfolio model based on uncertainty theory and provide the equivalent form of the model. Furthermore, we make a comparison of the optimal expected return between portfolio investment with options and without options. An important conclusion is reached: The portfolio investment with options produces a no less expected return than that without options. In addition, we make sensitivity analysis and get two vital corresponding results. As an illustration, a numerical example is presented as well. The numerical results reveal that the options should be considered in portfolio investment. And the call option with maximum exercise price is most valuable per premium cost with the same exercise date.