Research On The Application Of Robust Optimization For Portfolio Selection

The optimal investment strategy of portfolio model is sensitive to the input parameters like the expected return and covariance matrix of risk assets. The small changes of parameters may lead large variations in the composition of optimal portfolio. These optimal investment strategies are unreliable in practice of portfolio without consideration of uncertain parameters. Therefore, robust optimization theory attracts the attention of scholars as an effective approach to solve the problem of uncertain parameters in portfolio model. Compared with the traditional approach which supposes the uncertain parameters are random variable, robust optimization avoids the difficulty of estimate the distribution of random variable. The essence of robust optimization is to describe the uncertain parameters in model as simple geometrical form, so the original programming problem becomes the certain problem. No matter what the values of uncertain parameters are, the final investment strategy can partly ensure the optimality.First, we define the robust efficient solution and robust weak efficient solution from the point of view of multi-objective programming and construct robust multi-objective mean absolute deviation portfolio model with uncertain sets of box and ellipsoid. Because multi-objective programming needs to transform into single objective programming for solving model, we study the influence of weighted-sum method and ?-constraint method on the robust weak efficient solution of robust mean absolute deviation model. Then, we study the efficiency loss of robust frontier compare to the original nominal frontier.Second, we begin an empirical analysis on the original and robust mean absolute deviation portfolio model with two kinds of uncertain sets. We compare future stock returns of original and robust portfolio model under conditions of different length of time, different types of markets, different absolute deviation and different β value. The results show that ellipsoid set, most of time, can gain the solutions which is similar to original solutions. Meanwhile, the future stock return of robust investment strategy can not guarantee the advantage than original strategy.Finally, we consider that the investor faces many the limits of reality in actual investment, like the total amount of purchase, the minimum purchase quantity, the amount of unit purchase, the decision preference of investor, the amount of asset and the transaction cost. Meanwhile, with the development of the risk measure approach, mean-CVaR portfolio model emerge as the time require. Comparing with VaR, CVaR avoids the disadvantages of non-convexity and non-subadditive and can transform into liner programming model. Therefore, we construct a mean-CVaR portfolio model with complex constraints in ellipsoid uncertain set. Because this model belongs to NP-Hard problem and traditional algorithm can not solve it easily, we consider the particle swarm algorithm which has the advantages of simple form, fast convergence and easy to solve.To avoid the problems of premature convergence and falling into local optimal solution, we improve the basic particle swarm algorithm with the method of dynamic inertia weight, dynamic acceleration factor and mutation operation.