The Dalang-Morton-Willinger Theorem

Freddy Delbaen () and Walter Schachermayer ()
Additional contact information
Freddy Delbaen: ETH Zürich
Walter Schachermayer: Technische Universität Wien

Chapter 6 in The Mathematics of Arbitrage, 2006, pp 85-109 from Springer

Abstract: In Chap. 2 we only dealt with finite probability spaces. This was mainly done because of technical difficulties. As soon as the probability space (Ω,ℱ T ,P) is no longer finite, the corresponding function spaces such as L1(Ω,ℱ T ,P) or L∞(Ω,ℱ T ,P) are infinite dimensional and we have to fall back on functional analysis. In this chapter we will present a proof of the Fundamental Theorem of Asset Pricing, Theorem 2.2.7, in the case of general (Ω,ℱ T ,P), but still in finite discrete time. Since discounting does not present any difficulty, we will suppose that the d-dimensional price process S has already been discounted as in Sect. 2.1. Also the notion of the class ℋ of trading strategies does not present any difficulties and we may adopt Definition 2.1.4 verbatim also for general (Ω,ℱ T ,P) as long as we are working in finite discrete time. In this setting we can state the following beautiful version of the Fundamental Theorem of Asset Pricing, due to Dalang, Morton and Willinger [DMW 90].

Date: 2006
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:sprfcp:978-3-540-31299-4_6

Ordering information: This item can be ordered from
http://www.springer.com/9783540312994

DOI: 10.1007/978-3-540-31299-4_6

Access Statistics for this chapter

More chapters in Springer Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().