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Convergence of discretized stochastic (interest rate) processes with stochastic drift term

✍ Scribed by Deelstra, G. ;Delbaen, F.

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 118 KB
Volume: 14
Category: Article
ISSN: 8755-0024
DOI: 10.1002/(sici)1099-0747(199803)14:1<77::aid-asm338>3.0.co;2-2

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✦ Synopsis

For applications in finance, we study the stochastic differential equation dX

) dB Q with a negative real number, g a continuous function vanishing at zero which satisfies a Ho¨lder condition and a measurable and adapted stochastic process such that R S du( R a.e. for all t31> and which may have a random correlation with the process X itself. In this paper, we concentrate on the Euler discretization scheme for such processes and we study the convergence in ¸-supnorm and in H-norm towards the solution of the stochastic differential equation with stochastic drift term. We also check the order of strong convergence.

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Long-term returns in stochastic interest

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

✍ Deelstra, Griselda ;Delbaen, Fred 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 92 KB

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