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 .
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 (no transaction costs) and one illiquid risky asset (proportional transaction costs). We fully characterize the optimal trading and consumption strategies in terms of the solution of the free boundary ODE with an integral constraint. We find an explicit characterization of model parameters for the well-posedness of the problem, and show that the problem is well-posed if and only if there exists a shadow price process. Finally, we describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset .
A
(no transaction costs)
R
Using the shadow price approach, we
We
R
a
the
R
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
We find an explicit characterization of model parameters for the well-posedness of the problem, and show that the problem is well-posed if and only if there exists a shadow price process. Finally, we describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset