Special Semester on Stochastics with Emphasis on Finance
Linz, September 2008 - December 2008
Presentation: Generalization of the Dybvig-Ingersoll-Ross Theorem and Asymptotic Minimality

Workshop: Concluding Workshop

Time: Wed, December 03, 2008, 09:30-10:15

Speaker: Uwe Schmock


The long-term limit of zero-coupon rates with respect to the maturity does not always exist. In this case we use the limit superior and prove corresponding versions of the Dybvig–Ingersoll–Ross, which says that long-term spot and forward rates can never fall in an arbitrage-free model. Examples of models needing this generalization are presented. In addition, we discuss several definitions of arbitrage, prove asymptotic minimality of the limit superior of the spot rates, and illustrate our results by several continuous-time short-rate models. (Joint work with V. Goldammer.)

Presentation slides: http://www.fam.tuwien.ac.at/~schmock/Dybvig-Ingersoll-Ross.html

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