Optimal consumption and investment under transaction costs

We consider the Merton problem in a market with a single risky asset and proportional transaction costs and give a complete solution of the problem up to the solution of a first-crossing problem for a first-order differential... [ view full abstract ]

We consider the Merton problem in a market with a single risky asset and proportional transaction costs and give a complete solution of the problem up to the solution of a first-crossing problem for a first-order differential equation. A precise condition for when leverage occurs is provided. One new and unexpected result is if the model parameters are such that the solution to a standard Merton problem involves a leveraged position, and when transaction costs are large, the location of the boundary at which sales of the risky asset occur is independent of the transaction cost on purchases.