Optimal consumption and investment problems under GARCH with transaction costs

General multiperiod optimal consumption and investment problems with proportional transaction costs are investigated in this paper, a GARCH-type process is used to model the risky asset’s return series so that its time-varying moments and conditional heteroskedasticity can be properly described. We model this kind of consumption and investment problems as dynamic stochastic optimization problems, which can easily cope with different utility functions and any number of time periods. The procedure to efficiently solve the resulting nonlinear stochastic optimization problem is discussed in detail and a parallelizable decomposition algorithm is devised. Numerical results show the suitability and promise of our methodology. Copyright Springer-Verlag 2005