Actuarial Model Under Stochastic Interest Rate

Insurance is a commercial act.First of all,according to the insurance contract,the insured pay the money to the insurance company that the purpose is to prevent the loss of property.In the contract in accordance with the accident may result in the premium is to compensate for the loss by establishing an insurance fund.Usually in the calculation of the premium and the insured amount,the interest rate is assumed.But in real life,especially life insurance,the insurance is always a long-term process.The interest rate is not a fixed value,which usually influenced by the national macro policy such as fiscal policy,monetary policy and market fluctuations.Therefore,there is a certain difference between fixed interest rate and stochastic interest rate.With the fierce competition in society,the number of insurance companies is increasing,and the measurement and management of interest rate risk is more and more important.The study of stochastic interest rate is an important issue in the life insurance industry.In 2006,Xu Jun [17] of Wuhan University has written paper about the stochastic interest rate under Wiener and Homogeneous Poisson process connection in continuous conditions.On this basis,I made a promotion considering the limitation that the mean value of the Homogeneous Poisson process can't be changed with time.I chose the Non-homogeneous Poisson process.The first chapter mainly introduced the background knowledge and research purposes.The second chapter and the third chapter introduced the basic knowledge.In the fourth chapter,I calculated the first moment and the second order moment of the Life Annuity under Brown motion and Non homogeneous Poisson model.At last,I calculated the special pension and loss variable under the stochastic interest rate model.