Abstract
This paper discusses a stochastic programming approach for a multi-period portfolio optimization problem. Hibiki (2001) advocates the simulation/tree hybrid model for solving a multi-period optimal asset allocation problem with Monte Carlo simulation. We propose a linear approximation model based on the hybrid model, and compare it with other optimization models in the numerical examples, such as the stochastic programming models (i.e., the simulation model and the hybrid model), continuous-time models in which analytical solutions can be derived, and a Monte Carlo regression model proposed by Brandt et al. (2005). The results show better values can be derived in the linear approximation model than other models in the problems of CRRA utility function and the first-order lower partial moment which is one of the downside risk measure. In addition, the investment ratio at the initial time has got closer to the analytical solution. The objective function value of our model is improved in comparison with the hybrid model under the same scale problem. Especially in the CRRA case, the expected utility is larger and the investment ratio dependent of the state has become closer to the analytical solution than the Monte Carlo regression model. These results indicate that our model has the desirable properties for solving a multi-period portfolio optimization problem.
