Long‐term returns in stochastic interest rate models: different convergence results

Griselda Deelstra and Fred Delbaen

Applied Stochastic Models and Data Analysis, 1997, vol. 13, issue 3‐4, 401-407

Abstract: In this paper, we focus on different convergence results of the long‐term return (1/t)∫t0rudu, 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)∫t0Xudu, where (Xu)u⩾0 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 (Yn)n⩾1 with (Ynt)t⩾0=[(−2β3 δ¯n)1/2∫nt0(Xu+δu 2β) du]t⩾0 By the Aldous criterion, this sequence converges in law to a Brownian motion. These convergence results have some immediate applications. © 1998 John Wiley & Sons, Ltd.

Date: 1997
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https://doi.org/10.1002/(SICI)1099-0747(199709/12)13:3/43.0.CO;2-L

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmda:v:13:y:1997:i:3-4:p:401-407

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