Optimization of N-risky asset portfolios with stochastic variance and transaction costs

We examine the intertemporal optimal portfolio selection and consumption rule of an investor with a constant relative risk aversion who faces proportional transaction costs when trading between a risk-free asset and N risky assets. The investor's objective is to maximize the total utility of consumption over a fixed time interval [0, T]. Stochastic dynamic programming is applied to transform the problem into the Hamilton-Jacobi-Bellman equation and perturbation analysis is used to obtain the transaction boundaries and the consumption rule to leading order. We also consider the effect of the stochastic variance on the optimal allocation, where we provide an approximation scheme to determine the transaction boundaries for a portfolio with N risky assets. Numerical examples for a portfolio with a risk-free asset and two risky assets are also provided for constant variance as well as stochastic variance.