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

This paper makes two modest observations concerning a new formulation of the consumption and portfolio choice model of Merton (1971), with transactions costs. Suppose the agent 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._x000B__x000B_(1) With lump sum plus proportional costs, the optimal interval of time between transactions varies non-trivially with current wealth._x000B__x000B_(2) If, at each transaction, the agent is charged a fixed fraction of current wealth, an optimal policy exists and the optimal interval of time between transactions is fixed, independent of time and current wealth. That is, the optimal behavior is observationally equivalent to that of a pure discrete-time model, with an endogenously determined time interval