Pricing Research Of Mortgage Insurance

Mortgage is an effective way to settle the question of individual housing and start up housing consumption.It has a great progress in recent years,but the risk has been exposured. It is necessary to develop mortgage insurance now .In this paper,we research the pricing of two kinds of mortgage insurance , and discuss them under several models. Introducing the principle of option pricing ,we obtain the accurate pricing formulas to two kinds of mortgage insurance under six models. Further more,in first two models,we obtain the relation between the martingale pricing formulas and the insurance actuary pricing formulas.In detail we have main conclusions in this paper as follows:1. Obtain the martingale pricing formulas and the insurance actuary pricing formulas to two kinds of mortgage insurance ,and also prove that they go all the way when the unpaid money is a constant and the house price is driven by a genegal Ito process.2. Obtain the martingale pricing formulas and the insurance actuary pricing formulas to two kinds of mortgage insurance ,and also prove that the insurance actuary pricing are arbitrage when the unpaid money is a constant and the house price is driven by 0-U process.3. Obtain the martingale pricing formulas to two kinds of mortgage insurance under the Vasicek model when the unpaid money is a constant and the house price is driven by a genegal Ito process.4. Obtain the special martingale pricing formulas to two kinds of mortgage insurance when the unpaid money is a constant and the house price is given by the combination of a log-normal stochastic volatility process and an compound Poisson process.5. Obtain the martingale pricing formulas to two kinds of mortgage insurance when the unpaid money and the house price are driven by two correlative Ito processes respectively.6. Obtain the insurance actuary pricing formulas to two kinds of mortgage insurance when the unpaid money is driven by genegal Ito process and the house price is driven by nonhomo geneous Poisson jump-diffussion process.