# Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation

@article{Deng2019GeneralizedAI, title={Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation}, author={Shounian Deng and Chen Fei and Weiyin Fei and Xuerong Mao}, journal={Physica A: Statistical Mechanics and its Applications}, year={2019} }

Abstract In this paper, we consider a generalized Ait-Sahalia interest rate model with Poisson jumps in finance. The analytical properties including positivity, boundedness and pathwise asymptotic estimations of the solution to this model are investigated. Moreover, we prove that the Euler–Maruyama (EM) numerical solution converges to the true solution of the model in probability. Finally, we apply the EM solution to compute some financial quantities. A numerical example is provided to… Expand

#### 6 Citations

First order strong approximation of Ait-Sahalia-type interest rate model with Poisson jumps

- Computer Science, Mathematics
- ArXiv
- 2021

It is shown that the TJABEM can preserve the domain of the underlying problem for Ait-Sahalia-type interest rate model with Poisson jumps with non-globally Lipschitz drift and diffusion coefficients. Expand

Efficient approximation of SDEs driven by countably dimensional Wiener process and Poisson random measure

- Computer Science, Mathematics
- ArXiv
- 2021

This paper deals with pointwise approximation of solutions of stochastic differential equations (SDEs) driven by infinite dimensional Wiener process with additional jumps generated by Poisson random measure and establishes matching (up to constants) upper and lower bounds for ε-complexity. Expand

Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations

- Economics
- 2021

In this paper, we study analytical properties of the solutions to the generalised delay AitSahalia-type interest rate model with Poisson-driven jump. Since this model does not have explicit solution,… Expand

Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift

- Computer Science, Mathematics
- Appl. Math. Comput.
- 2021

The existence and uniqueness of strong solutions of jump-diffusion stochastic differential equations with discontinuous drift coefficient and a possibly degenerate diffusion coefficient are proved. Expand

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

- Computer Science, Mathematics
- Numer. Algorithms
- 2021

The mean-square convergence rate of the backward Euler method (BEM) for a generalized Ait-Sahalia interest rate model with Poisson jumps is revealed and it is shown that the BEM preserves the positivity of the original problem. Expand

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