Optimal Investment with Transaction Costs and Stochastic Volatility

Abstract: We analyze the joint impact of transaction costs and uncertain volatility on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when the cost is small. Under stochastic volatility, but with no transaction costs, the Merton problem under general utility functions can also be analyzed with multiscale methods. Here, we look at the long-run growth rate problem when both frictions are present, using separation of time scales approximations. This leads to perturbation analysis of an eigenvalue problem. We find and interpret the first two terms in the asymptotic expansion in the time scale parameter, of the optimal long-term growth rate, and of the optimal strategy, for fixed transaction costs.

Joint work with Maxim Bichuch (WPI)