AN OPTIMAL CONTROL FORMULATION OF PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COST

Abstract. This paper formulates a consumption and investment decision problem for an individual who has available a riskless asset paying fixed interest rate and a risky asset driven by Brownian mo-tion price fluctuations. The individual is supposed to observe his or her current wealth only, when making transactions, that trans-actions incur costs, and that decisions to transact can be made at any time based on all current information. The transactions costs is fixed for every transaction, regardless of amount trans-acted. In addition, the investor is charged a fixed fraction of total wealth as management fee. The investor’s objective is to max-imize the expected utility of consumption over a given horizon. The problem faced by the investor is formulated into a stochastic discrete-continuous-time control problem. Key words: transaction cost, continuous-discrete-time, stochastic optimal control problem 1