The Logarithmic Utility of Transaction Costs and the Selection of Dynamic Investment Portfolio

Abstract

AbstractThe selection dynamic portfolio, Bankruptcy and the Logarithmic Utility of Transaction Costs have been extensively studied, which includes a risk-free asset and risky asset, whose price is dynamic geometry by the control of Brown motion. Investors paid transaction cost as a risk asset transactions (linear function), whose goal is to find the stochastic control in the risky and risk-free assets investment amount, maximized the discounted utility expected value of the terminal wealth. But as optimal control problems of a non singular stochastic, in this sense, the conditions necessary for optimal resulted determined relationships in clear control and value function. The Control of the purchase and sale of risk assets is bounded, and proportional transaction costs is controlled by a single formula, which control the rates of the purchase and sale of risk assets. Numerical results indicate that one of the interfaces between purchase and sales, in which a constant determined the best selection of the relationship.KeywordsDynamic investment portfolioTransaction costLogarithmic utilityFunction analysis