عنوان مقاله [English]
In this paper, we introduce two robust models to create a portfolio with the best combination of risk free asset, stocks and options within multi-periods.Many input parameters of model, such as stocks or options price, are uncertain. If they are estimated as deterministic values, portfolio optimization may result in infeasible solution. Among different approaches for handling uncertainties, we adopt robust optimization.First, as a basic model, we formulate the problem with deterministic data. The decision variables are the amount invested in the free risk asset, the number of stocks as well as the number of options (both call and put) to include in the desired portfolio. The objective is to determine the optimal combination of assets in order to maximize the total return at the end of last period. The constraints represent the limitation on initial investment budget in the first period; the available budget at the end of each period which includes new investment opportunity for next period plus the return of existing investment and finally the constraint that calculates final return of portfolio. No shortselling is allowed.For developing the robust model, uncertainty of stock prices at the end of each investment period are presented within linear intervals.In the first model, we develop a robust counterpart which results in the best solution, if the worst situation within the intervals occurs. It is a conservative counterpart robust model in which the relations between the uncertain parameters, such as the value stocks and options, is nonlinear (linear piecewise).In the second model, each constraint has a special set of uncertain parameters which works independently from the other constraints. Therefore, for controlling the feasibility of solution, each one must be considered separately. This model is a robust counterpart of for multi-period and option based portfolio optimization problems. Optimal solution of this model is feasible for each combination of stock value for future periods. The optimal solution shows the best solution of the model for the worst combination of sock value for future periods. However, we consider an upper limit for protection level of uncertainties of all constraints. In fact, for dealing with this problem and improving our model, we introduce a controlling factor for investor risk acceptance in investment. It is clear the chance of realization of the worst case stock value combination at each period is very low.In the second model, we adopt a different approach to develop a counterpart model which is controllable, as far as its conservative degree is concerned. To handle uncertain nonlinear parameters, we introduce a new approach to develop the proposed modes.To solve the models, they are reformulated as dual problems. In this way, the optimal solution can be obtained analytically.To analyze the models, we solve three problems with 100 stocks and 400 options and study the results.