Multiperiod consumption and portfolio decisions under the multivariate GARCH model with transaction costs and CVaR-based risk control

Abstract.

This paper examines the modelling and solution method of complex multiperiod optimal consumption and investment problems with several kinds of constraints. Our work differs from previous results in several ways: typical market imperfections such as short sale constraints, proportional transaction costs are considered simultaneously; the MGARCH model is adopted to provide a satisfactory description of the time-varying behavior of stock returns; the CVaR constraint is introduced to control the wealth loss risk while maximizing the expected utility; it is assumed that the investor wants to maximize the expected utility of both his intermediate consumptions and his terminal wealth; most importantly, the considered problem is described as a stochastic programming problem, which can easily cope with problems with arbitrary utility functions, multiple risky assets and many periods. The derived model can help the investor to find robust consumption-investment decisions. The procedure to solve the resulting nonlinear stochastic optimization problem is discussed in detail. Numerical results show the suitability and promise of our methodology.