Abstract
In this paper, we consider the robust portfolio selection problem which has a data uncertainty described by the $(p,w)$ -norm in the objective function. We show that the robust formulation of this problem is equivalent to a linear optimization problem. Moreover, we present some numerical results concerning our robust portfolio selection problem.
Highlights
Portfolio selection is the problem of allocating capital over a number of available assets in order to maximize the return on the investment while minimizing the risk
When the realized asset returns are less than the estimates used to optimize the model, the realized portfolio return will be less than the optimal portfolio return given by the objective
We see that the robust formulation of this problem is a linear optimization problem
Summary
Portfolio selection is the problem of allocating capital over a number of available assets in order to maximize the return on the investment while minimizing the risk. Μi and σi are treated as known constants; asset returns are variable. It is reasonable to conclude that a model which treats returns as known constants will produce a portfolio whose realized return is different from the optimal portfolio return given by the objective function value. When the realized asset returns are less than the estimates used to optimize the model, the realized portfolio return will be less than the optimal portfolio return given by the objective. It is worthwhile exploring alternative frameworks, such as robust optimization, for application to the portfolio selection problem
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