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

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 . 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 $p$th moment boundedness of the solution of BIM. Finally, we illustrate those results in the last section.