Research On The Actuarial Pricing Models Of Reverse Mortgage With The Continuous Compound Interest

In recent years, reverse mortgage business has been gradually introduced into China and has been launched in partial tier cities. The problem of partial elderly pension can be alleviated. Undoubtedly, reverse mortgage is chosen by investor to invest as a new type of pension financial products, with the proposing of the internet finance, the adjusting of the deposit-reverse ratio and interest rates that operate by the central bank. It is imperative to enrich its business types. Based on this, the paper studies the actuarial pricing model of the reverse mortgage from the view of redeemable and non-redeemable with the way of the continuous compound interest.Firstly, according to reverse mortgage loan pricing and American call option pricing theory, the way of the traditional discrete interest are improved, the paper built the payment pricing model and the annuity pricing model of single-life and double-lives under no foreclosure, as well as, the above models of redemption are established.Secondly, combining the standard Wiener process with the Poisson process, the paper rebuilds the accumulation function of interest force. Based on the fixed interest rate and continuous interest model, the irredeemable payment pricing model and the non-redeemable annuity pricing model of single-life and double-lives are presented with the stochastic interest rate. Then the paper built the foreclosure actuarial pricing models innovative under the same conditions.Thirdly, in order to study the nature of reverse mortgages pension pricing effectively and analyze the models sufficiently by using experiential mortality table, the paper assumed the assumption of death force evenly distributed (referred UDD) for the age at death , and deduced the irredeemable payment pricing model and the non-redeemable annuity pricing model of single-life and double-lives respectively with the fixed interest rates and stochastic ones which lay the foundation for the subsequent numerical analysis by the way of the continuous compound interest.Finally, in the numerical simulation, the initial values of parameters were set up by collecting data, and MATLAB was applied to calculate the irredeemable pricing models with the UDD assumption. Through comparing the difference between the continuous actuarial pricing model of single-life and doubt-lives, the results showed that the single loan amount is less than the couple jointly apply for loan values, that is, if there are plans to apply for reverse mortgage business, it should make property rights owned by individuals, which is beneficial to the borrower. In addition, the analysis of sensitivity to parameter for the continuous irredeemable actuarial pricing models with the fixed interest rate indicated that the actuarial pricing of continuous irredeemable reverse mortgages are more sensitive to the variation of interest rate. At last, comparing the influence of the loan due to the change of different parameters for the continuous irredeemable actuarial pricing models with stochastic interest rate, the thesis states that the constructed models conform to the actual situation and reflected the value of the foreclosure actuarial pricing models indirectly.