Convergence and non-negativity preserving of the solution of balanced method for the delay CIR model with jump

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:344

Article

Aghda, A. S. Fatemion¹  Hosseini, Seyed Mohammad¹  Tahmasebi, Mahdieh¹ 

[1] Tarbiat Modares Univ, Dept Appl Math, POB 14115-175, Tehran, Iran

关键词: Stochastic delay differential equation (SDDE) with jump;    The delay CIR model with jump;    Balanced method;    Convergence;    Non-negativity;    Moment boundedness;   

DOI  :  10.1016/j.cam.2018.06.009

来源: Elsevier

【 摘 要 】

In this work, we propose the balanced implicit method (BIM) to approximate the solution of the delay Cox-Ingersoll-Ross (CIR) model with jump which often gives rise to model an asset price and stochastic volatility dependent on past data. We show that this method preserves non-negativity property of the solution of this model with appropriate control functions. We prove the strong convergence and investigate the pth moment boundedness of the solution of BIM. Finally, we illustrate those results in the last section. (C) 2018 Published by Elsevier B.V.

【 授权许可】

Free