Study Of The Dual Randomness For Automatic Investment Plan Of Mutual Fund Theory And Annuity Theory

For automatic investment plan (AIP) of mutual fund theory and annuity theory, interest rate and the term of investing or morality are two key random factors and they are very important for calculating and evaluating benefits and risks. In this paper,the present value and the risks of automatic investment plan of mutual fund and annuity have been established for insurance company, which gets profits by AIP and pays for annuity.AIP gets benefits for investors by investing regularly on some special mutual fund and sells off in same time. Here we conduct a dual random model for its benefits and get some mathematical characters. For annuity we also get a model for analysing the amount of paying out with the random factors of interest rates and morality.In this paper, we conduct those models on the side of insurance company for expecting its benefits and payment, and the difference between them is very important for the company's development and risk. In the last of the paper, we build the risk on the different liquidity between the mutual fund and annuity, and get a new way for describing the risk for insurance company.