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On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps

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Abstract

This article aims to reveal the mean-square convergence rate of the backward Euler method (BEM) for a generalized Ait-Sahalia interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves the positivity of the original problem. Furthermore, we successfully recover the mean-square convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, China

    Yuying Zhao, Xiaojie Wang & Mengchao Wang

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  1. Yuying Zhao
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  2. Xiaojie Wang
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  3. Mengchao Wang
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Correspondence to Mengchao Wang.

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This work was supported by Natural Science Foundation of China (12071488, 11671405, 11971488, 91630312), Innovation Program of Central South University(No.2019zzts397), and Natural Science Foundation of Hunan Province for Distinguished Young Scholars (2020JJ2040).

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Zhao, Y., Wang, X. & Wang, M. On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps. Numer Algor 87, 1321–1341 (2021). https://doi.org/10.1007/s11075-020-01009-1

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  • DOI: https://doi.org/10.1007/s11075-020-01009-1

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