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This paper discusses an optimal transaction interval for 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 motion price fluctuations. The individual observes current wealth when making transactions, that transactions 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 transacted. In addition, the investor is charged a fixed fraction of total wealth as management fee. The investor’s objective is to maximize the expected utility of consumption over a given horizon. The problem faced by the investor is formulated in a stochastic discrete-continuous-time control problem. An optimal transaction interval for the inverstor is derived.

AN OPTIMAL TRANSACTION INTERVALS FOR PORTFOLIO SELECTION PROBLEM WITH BULLET TRANSACTION COS