Actuarial Pricing Models of Reverse Mortgage with the Stochastic Interest Rate

The aging problem became more important and serious in China in recent years. The reverse mortgage is an innovation model to support the aged people. In this study, the accumulation function model of interest force with a Wiener process and a negative-binomial distribution is proposed as the basis for the reverse mortgage. With the proposed model, a lump sum pricing model, annuity pricing model, linear increasing annuity pricing model for single-life and double-lives are provided. All of the models can be improved to solve the problem that the actuarial pricing models of reverse mortgage only could be calculated by the fixed interest rate. LS : The amount of the loan which is got by one borrower with a method of payment with the stochastic interest rate. ' PMT : The amount of the loan which is got by one borrower at the beginning of each year with the method of annuity under the stochastic interest rate. ' PMTA : The amount of the loan which is got by one borrower at the beginning of the first year by linear increasing annuity with the stochastic interest rate. Q: The increasing amount every year of the loan when get the loan by linear increasing annuity. d: The increasing ratio every year of the loan when get the loan by equal ratio increasing annuity. xy LS ' : The amount of the loan which is got by two borrowers by a sum of loan ceiling with the stochastic interest rate. xy PMT ' : The amount of the loan which is got by two borrowers at the beginning of each year by annuity with the stochastic interest rate. xy