092061 (E50, M12) A tractable term structure model with endogenous interpolation and positive interest rates : Schlöegl E., Presented at the International Workshop on The Interplay between Insurance, Finance and Control, organized by the Mathematical Research Centre at Aarhus University, also supported by the Danish Science Research Council and the Centre for Analytical Finance

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 190 KB
• Volume: 20
• Category: Article
• ISSN: 0167-6687
• DOI: 10.1016/s0167-6687(97)80684-1

✦ Synopsis

semi-martingale S the condition of No Free Lunch with

Vanishing Risk is equivalent to the existence of an equivalent local martingale measure for the process S. It was asked whether the local boundedness assumption on S may be dropped. In recent joint work with F. Delbaen, the authors have shown that if they drop in this theorem the local boundedness assumption on S the theorem true if they replace the term equivalent local martingale measure by the term equivalent sigma-martingale measure. The concept of sigma-martingales was introduced by Chou and Emery -under the name of "semimartingales de la classe (~m)''" The authors provide an example which shows that for the validity of the theorem in the non locally bounded case it is indeed necessary to pass to the concept of sigma-martingales. On the other hand, they also observe that for the applications in Mathematical Finance the notion of sigmamartingales provides a natural framework when working with non locally bounded processes S.