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Title:A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets PDF Logo
Authors:Irle, Albrecht
Prelle, Claas
Issue Date:2008
Series/Report no.:Kiel working paper 1449
Abstract:We consider a portfolio optimization problem in a Black-Scholes model with n stocks, in which an investor faces both fixed and proportional transaction costs. The performance of an investment strategy is measured by the average return of the corresponding portfolio over an infinite time horizon. At first, we derive a representation of the portfolio value process, which only depends on the relative fractions of the total portfolio value that the investor holds in the different stocks. This representation allows us to consider these so-called risky fractions as the decision variables of the investor. We show a certain kind of stationarity (Harris recurrence) for a quite flexible class of strategies (constant boundary strategies). Then, using renewal theoretic methods, we are able to describe the asymptotic return by the behaviour of the risky fractions in a typical period between two trades. Our results generalize those of [4], who considered a financial market model with one bond and one stock, to a market with a finite number n>1 of stocks.
Subjects:Portfolio theory
transaction costs
Harris recurrence
renewal theory
JEL:G11
C61
Document Type:Working Paper
Appears in Collections:Kieler Arbeitspapiere, IfW
Publikationen von Forscherinnen und Forschern des IfW

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