Kiel Working Papers, Kiel Institute for World Economics
No 1449:
A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets
Claas Prelle and Albrecht Irle
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; (follow links to similar papers)
JEL-Codes: G11,; C61; (follow links to similar papers)
28 pages, September 2008
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