Constant Rebalanced Portfolio Optimization under Nonlinear Transaction Costs

In this paper, we study a multi-period portfolio optimization where the conditional value-at-risk (CVaR) is controlled as well as the expected return, and the so-called constant rebalancing strategy is employed under nonlinear transaction costs. In general, the optimization of the strategy itself is, however, difficult to attain a globally optimal solution because of the nonconvexity. In addition, nonlinearity of the transaction cost and the CVaR functions makes things worse, and even a locally optimal solution may not be reached via a state-of-the-art nonlinear programming solver when the size of the problem is large. In order to provide a practical solution to the highly complex problem, we propose a local search algorithm where linear approximation problems and nonlinear equations are iteratively solved. Computational results are presented, showing that the proposed algorithm attains a good solution in practical time even when a revised version of an existing global optimization approach cannot return any feasible solution.