The Study Of The Reserve With Controlled Random Interest Rates

Firstly, we assum that the interest rate is controlled in an interval [a, b], where a>0is the minimum interest rate, b is the highest point of interest rate; When the interest rates decline or rose to a or b,the bank will adjust the interest rate level to achieve the macroeconomic regulation and control the goal. Assuming a stochastic process X under the following conditions, when interest rates reach the b point, the random process X has the nature of the reflected Brownian motion, when interest rates fell to level of a,X is related to nature of the Brownian motion. Then on the premise of those two assumptions, we further consider the effects of mortality on reserves.We suppose the force of mortality is constant.Using the financial random analysis and properties of (reflected) Brownian motion and reserve theory in actuarial mathematics, we construct a continuous insurance reserve model, on the basis of life-table data using MATLAB software for data analysis and simulation, compare with fixed interest rate of reserves model.Secondly considering the force of mortality model with surrender,due to the surrender of the insured will adversely affect the operation of the insurer, the insurance companies in the extraction of reserve also need to consider the surrender happening, in actual other factors(as procedures fee, commissions cost, general risk, other factors)of effect, directly calculation of the surrender amount will be difficult, so this article considers combining surrender to mortality factors, generally we suppose the force of mortality is μ,after considered the surrender situation, that is equal to enhance the original force of mortality, the new force of mortality has supposed to be μ*=rμ(r>0).Under the new force of mortality we give the reserve model and simulate by MATLAB software under the different interests and the scale factor of reserves.Finally, on the condition of the force of mortality submit to DE MOIVRE, considering death compensation payment for continuous incremental form over time, we give the reserve model in the case of interest rate controlled. Based on2009mixed life tables’data, we use MATLAB software for data simulation and give the reserve figure in the different ages.