Long-term returns in stochastic interest rate models: different convergence results
✍ Scribed by Deelstra, Griselda ;Delbaen, Fred
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 92 KB
- Volume
- 13
- Category
- Article
- ISSN
- 8755-0024
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✦ Synopsis
In this paper, we focus on different convergence results of the long-term return (1/t) R r S du, where the short interest rate r follows an extension of the Cox-Ingersoll-Ross (1985) model. Using the theory of Bessel processes, we proved the convergence almost everywhere of (1/t) R X S du, where (X S ) SV denotes a generalization of a Besselsquare process with drift. We also studied the convergence in law of the long-term return in order to make some approximations. We observed the convergence in law of the sequence of processes (½L) LV with
RV By the Aldous criterion, this sequence converges in law to a Brownian motion. These convergence results have some immediate applications.