Albrecht Irle, Claas Prelle:

A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets

We consider a portfolio optimization problem in a Black-Scholes model with n stocks, in which an investor faces both fixed and proportional trans- action costs. The performance of an investment strategy is measured by its asymptotic return

where X_t denotes the portfolio value at time t. At first, we derive a representation of the value process, which does not depend on absolute values, but only 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 and plausible 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.

Mail an Jens Burmeister

[Thu Feb 19 18:56:37 2009]

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