The Logarithmic Utility of Transaction Costs and the Selection of Dynamic Investment Portfolio
The 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 tr
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The Logarithmic Utility of Transaction Costs and the Selection of Dynamic Investment Portfolio Zhengang Lu
Abstract The 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. Keywords Dynamic investment portfolio • Transaction cost • Logarithmic utility • Function analysis
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Introduction
In this paper, research on the logarithms effect of not- line portfolio choice problem and bargain cost as the not-strangely random superior control problem, while trading the cost as the superior essential condition, cause controlling of explicit relation and develop the value function of tool. These control a piece to purchase and sell risk property quantity, they all appear in the drift director dynamics equation; And produce from here of maximize a problem two times. The control is absolutely
Z. Lu (*) Siping Professional College, Siping 136002, China e-mail: [email protected] S. Zhong (ed.), Proceedings of the 2012 International Conference on Cybernetics 2073 and Informatics, Lecture Notes in Electrical Engineering 163, DOI 10.1007/978-1-4614-3872-4_264, # Springer Science+Business Media New York 2014
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continuous and have boundary. Again attain balance moment, therefore clinch a deal to lead is infinite, and say on this meaning, it is strange to clinch a deal to lead [1]. The HJB equation that produces from here causes a set of value function and its derivatives for involving as the superior inequality condition, but these match with Davis and promise Man, the bargain cost of the in the official records piece proportion. However, this is to have no necessity to solve these inequalities. Is contrary, the HJB equation solves Die generation to control two subitems because of the existence. The not-strange control comes to a decision the natural extension of the HJB equation of Mo to be worth function and says on this meaning from the HJB equation and pass the bargain cost of constitution parameter is zero, have never traded the portfolio of cost choice problem analysis research. This is be not with use establishment of under the circumstance the strange sup
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