 A renewal theoretic result in portfolio theory under transaction costs with multiple risky assetsAlbrecht Irle and Claas Prelle No 1449, Kiel Working Papers from Kiel Institute for the World Economy (IfW Kiel) 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. Keywords: Portfolio theory; transaction costs; Harris recurrence; renewal theory (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:zbw:ifwkwp:1449 Access Statistics for this paper More papers in Kiel Working Papers from Kiel Institute for the World Economy (IfW Kiel) Contact information at EDIRC. |
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