Abstract
Researchers in the field of portfolio optimization made efforts to decrease uncertainty in future returns. Any disturbance in the parameter values causes the solution to be non-optimal or impossible. This study designs a strong fuzzy-multipurpose model for stock portfolio optimization based on Tehran Stock Exchange market data. At the end of the paper, the created model is compared with the results of the multi-objective model. The results show that the fuzzy multi-objective optimization model has relative stability and model compared to the multi-purpose optimization model is strong.
Highlights
ObjectiveRobustness to objective function is special state of robustness to constraints. In other words by definition of a new variable z and by adding constraintc ( p ) x t , we reach an equivalent model (1)
Choosing the optimal investment portfolio is one of the most important issues in the field of financial issues in which an attempt is made to distribute a certain amount of capital among assets in order to achieve a specific goal or goals
If the input data in constraints have value except their nominal value, the constraint is violated or it is not feasible and if the input data of objective function are deviated from their nominal value, the optimization is ignored or optimal solution of nominal problem is not justified
Summary
Robustness to objective function is special state of robustness to constraints. In other words by definition of a new variable z and by adding constraintc ( p ) x t , we reach an equivalent model (1). The objectives (12), (13) consider investment constraint in each of securities (the max and min investment) and the term (14) focuses on maximization of sum of budget and portfolio return. 5-Fuzzy robust multi-objective programming model Ghahtarani, A., Najafi (2013) were not informed of the form of distribution of uncertain parameters and considered these parameters as stochastic value fluctuating in a symmetric interval. In their model, the middle value of interval is called as nominal value. The solution of maximum commonality of objective function and region is justified as achieved: max min[⋂xi=1 Di(x), G(x)].
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