| In traditional actuarial theory,the interest rate is constant,but in real life,because of the influence of government regulation and control,economic cycle,market fluctuation and other factors,the interest rate is random,and the small change of interest rate may bring large losses to insurance companies.It is important for insurance companies how to effectively avoid interest rate risk.Therefore,the interest rate is the focus of actuarial research,attracted many scholars to study.The main contents of this paper are as follows:(1)Considering the randomness of interest rate,the interest force model is established with the help of the stochastic analysis theory of bi-fractional Brownian motion.According to the Ito formula,the accumulation factor and discount factor are obtained.The actuarial present value of annuity and premium is studied and its analytical expression is obtained.Then the sensitivity of the model is analyzed.(2)Based on the bi-fractional Brownian motion and Poisson process,the interest force model is established,and the accumulation factor and discount factor are obtained by solving the model.The actuarial present value of annuity and premium under the model is studied,the analytical expression is obtained,and the sensitivity of the model is analyzed. |
PDF Full Text Request