Numeraire portfolios and utility-based price systems under proportional transaction costs

Jörn Sass () and Manfred Schäl ()

Decisions in Economics and Finance, 2014, vol. 37, issue 2, 195-234

Abstract: In a discrete-time incomplete financial market with proportional transaction costs and with independent and bounded returns, we prove the existence of a consistent price system that can be written as the expectation of the discounted claim under the real-world probability measure P and not just under a martingale measure. In fact, the claim is then discounted by some specific dynamic portfolio called the numeraire portfolio as in the classical case of markets without transaction costs. For that specific numeraire, P will be a martingale measure. Naturally, the concept of a numeraire portfolio has here to be adapted to the concept of consistent price systems for markets with transaction costs. Moreover, again as in the classical case, the numeraire portfolio can be chosen as log-optimal portfolio. The same analysis works for power utility functions. However, then a change of measure is necessary. This paper applies methods from stochastic dynamic programming to finance. Copyright Springer-Verlag 2014

Keywords: G11; G12; Numeraire portfolio; Power utility; Consistent price system; Proportional transaction costs; Dynamic programming (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10203-012-0132-8 (text/html)
Access to full text is restricted to subscribers.

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:spr:decfin:v:37:y:2014:i:2:p:195-234

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10203/PS2

DOI: 10.1007/s10203-012-0132-8

Access Statistics for this article

Decisions in Economics and Finance is currently edited by Paolo Ghirardato

More articles in Decisions in Economics and Finance from Springer, Associazione per la Matematica
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().