A Simple Model of Mortgage Insurance
用一个两期模型分析借款人如何选择最优的抵押贷款还款时间模式，考虑未来房价不确定性和保险保费与首付风险的关系，帮助理解不同时间偏好借款人的贷款选择。
This paper uses a two‐period model to analyze the borrower's choice of an optimal time pattern of mortgage payments in a world where future house values are uncertain. Since a decline in values can make the borrower's equity negative, leading to default on the mortgage, lenders in the model will require the purchase of mortgage insurance. The premium on the insurance policy will depend on the riskiness of the mortgage, which in turn depends on the magnitude of the initial mortgage payment. Mortgages with large (small) first payments will carry low (high) insurance premiums. Taking this fact into account, the borrower decides on the optimal riskiness of his mortgage. Borrowers who discount the future heavily choose risky mortgages carrying high insurance premiums, while those who place a higher value on future consumption opt for less risky contracts carrying low (or zero) premiums.