Optimal portfolio selection with transaction costs (Q2712223)

This paper considers a portfolio with a bank account paying a fixed rate of interest and \(n\) risky assets whose prices are modeled as geometric Brownian motions. The investor consumes at a rate \(c(t)\) from the bank account and is subject to the constraint that he remains solvent at all times. Any stock trading must be selffinancing, and there incurs a transaction cost being proportional to the amount being traded. The investor's objective is the maximization of his expected discounted utility of lifetime consumption.NEWLINENEWLINENEWLINEAfter the formulation and theoretical study of the portfolio selection problem, the singular control problem is transformed into a new problem involving only absolutely continuous controls using a random time change. It is shown that the value functions for the two problems are closely related and that the value function for the transformed problem is the unique viscosity solution to the corresponding Hamilton-Jacobi-Bellman equation. The Markov chain approximation to the transformed problem is also constructed and convergence of the value function of the transformed problem is established as the discretization parameter goes to zero.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].