Optimal investment and consumption with liquid and illiquid assets. (arXiv:1602.06998v1 [q-fin.MF])

We consider an optimal investment/consumption problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio which consists of one bond, one liquid risky asset and one illiquid risky asset (proportional transaction costs). Using the shadow price approach, we fully characterize the optimal trading and consumption strategies in terms of the solution of a free boundary ODE with an integral constraint. In the analysis, there is no technical assumption (except a natural one) on the model parameters. We also prove an asymptotic expansion result for small transaction costs.