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

Irle Albrecht and Prelle Claas
Additional contact information
Prelle Claas: Kiel Institute for the World Economy, Kiel

Statistics & Risk Modeling, 2009, vol. 27, issue 3, 211-233

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 [irl1], 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)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1524/stnd.2009.1049 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:27:y:2009:i:3:p:211-233:n:2

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1524/stnd.2009.1049

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().