Transactions Costs and Portfolio Choice in a Discrete - Continuous Time Setting

This paper makes the following observation concerning a new formulation of the consumption and portfolio choice model of Merton (1971), with transactions costs. Suppose an investor observes his or her current wealth only when making a transaction, that transactions are costly, and that decisions to transact can be made at any time based on all current information. If, at each transaction, the agent is charged a fixed fraction of current portfolio value, an optimal policy exists and the optimal interval of time between transactions is fixed, independent of time and current wealth. We thank Monique Pontier, Monique Jeanblanc-Picqué, and a referee for many suggestions and comments. Correspondence should be directed to Darrell Duffie at the Graduate School of Business, Stanford University, Stanford CA 94305-5015. This paper was written when Tong-sheng Sun, currently with Shearson Lehman Hutton, was at Stanford University. The paper reflects the views of the authors and should not be interpreted as reflecting those of Shearson Lehman Hutton. This is in the Research Paper Series, Graduate School of Business, Stanford University.