The Net Premium Of The Double-decrement In A Class Of Stochastic Interest Rate Model

In traditional actuarial theory,premium and reserve calculation and prediction of risk are mainly in the condition of fixed-interest rates.However,the financial services industry in the era of such rapid development,the interest rate changes at any time as the market,policy changes,therefore it is necessary to take into account the stochastic interest rates.In view of the importance of interest rates,many scholars have put forward a theory of term structure of interest rates and models to explain the behavior of interest rates.Especially,short-term interest rate has a direct impact on asset pricing,financial product design,hedge and risk management,arbitrage and speculative financial activities.Many term structure of interest rate models were proposed to characterize the random behavior of the interest rate.After Merton(1973), Vasicek(1977),Cox,Ingersoll and Ross(1985,CIR)'s pioneering research in the term structure of interest rates,Hull and White(1990),Jamshidiam(1995),Constantinides (1992),Duffie and Kan(1996),Longstaff and Schwartz(1992)also carried out a series of research and extension.In this paper,I discussed the net premium of the double-decrement in a class of stochastic interest rate model.First of all,I reviewed the development process of stochastic interest rates;In order to simplify the calculation process,I take the equilibrium model of Merton(1973)'s model to discussed the net premium of the single-decrement in the condition;And on this basis,I derived the net premium of the double-decrement in the condition of Merton(1973)'s model;Finally,I take out a practice example to illustrate the practical method of premium calculation.