Fuzzy Pricing Of Housing Reverse Mortgage

Housing reverse mortgage is an innovation financial tool designed for solvingpension problems for the elders who have real estate but lack of cash. The basicoperation is: people should mortgage their own real eastate to financial or insuranceinstitutions after retirement. They will obtain a lump sum or lifetime annuity until theyare dead. The financial institution will get the real estate after the elders die, andfinancial institution could make money by selling the house. if the price is higher thanthe entire principal and interst of the mortgage loans, financial institutions could getbenefit from reverse mortgage. This approach can be used as supplement of existingendowment resources.There are a lot of problem that we will be faced with if the reverse mortgagebusiness will run in China, one of the most important is how to reasonable pricing thereverse mortgage. Prior research prices reverse housing mortgage under stochasticactuarial model, while this paper considers the fuzziness of mortgage loan rate andhouse value increase rate. This paper treats the mortgage loan rate and house valueincrease rate are described as fuzzy numbers, and employs discrete mortality rate. Afterbuilding a fuzzy reverse housing mortgage model with fuzzy random variable, thispaper prices a lump sum loan and nominal payment loan respectively. Moreover,considering the flexibility of reverse mortgage product, this paper also prices reversemortgage with one borrower and two borrowers, and product with redemption right. Atthe end of this paper, a calculation example is given base on of Chinese history data.