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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Kiel Working Paper ; No. 1449

Classification and Topics

• Classification: Wirtschaft ; Portfolio Choice; Investment Decisions ; Optimization Techniques; Programming Models; Dynamic Analysis
• Subject: Portfolio theory ; transaction costs ; Harris recurrence ; renewal theory ; Portfolio-Management ; Strategie ; Transaktionskosten ; Black-Scholes-Modell ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Irle, Albrecht ; Prelle, Claas
• Event: Veröffentlichung
• (who): Kiel Institute for the World Economy (IfW)
• (where): Kiel
• (when): 2008

Further information

• Handle: http://hdl.handle.net/10419/24844
• Last update: 10.03.2025, 11:44 AM CET