Ümit modeli ile portföy seçimi

Decision making under uncertainty has always been important among the research community in industrial engineering. Many models which try to explain the attitude of decision maker under uncertainty have been proposed until today. The expected utility model is one of the most widely used models in this research area. However, some surveys show that people do not behave as stated in utility theory. So, non-expected utility models have recently become popular and the prospect model is one of them. The prospect model contradicts the expected utility model in a number of ways. Main theme of our research is to investigate the choices of prospect investors in a market that contains one risky and one risk-free asset. Exhibiting the differences between structures of the value functions, we get some indications about the portfolio choices of prospect investors. Firstly, we constructed a general model for the portfolio optimization problem within the frame of the prospect theory. Then, we analyzed it with the different types of value functions: piecewise linear, exponential and piecewise exponential, sequentially. Using different return distributions, each value function is investigated in more details. We derived the solution of the portfolio optimization problem and we obtained some interesting properties of optimal prospect portfolios. Looking at the relationship between the optimal portfolios and asset means, we show that there is a mean interval for a portfolio where it is optimal not to buy or shortsell the risky asset. Finally, we presented numerical examples to illustrate the shapes of the objective function. Moreover, comparing piecewise exponential and exponential optimal solutions, we analyzed the e¤ects of the prospect value functions.