Modification of interest rate model based on compound poisson process and brownian motion affected by inflation rate

In actuarial science, interest rate model based on compound Poisson process and Brownian motion is proposed to determine actuarial present value. We used inflation rate in interest rate model to obtain the behavioural change of interest rate model under different parameters based on inflation rate data of Bank Indonesia. The interest rate model can be used to determine actuarial present value of term life insurance for discrete life annuities. To confirm the analytical result, some numerical simulations are presented.