Pricing Reverse Mortgages under Exponential L'evy Processes

[[abstract]]本研究對反向房屋抵押貸款作訂價模型，針對此商品以及其主要風險做以介紹，目的將以往的房價過程服從布朗運動的想法加以修正，於是本文主要表達將房價服從指數Levy過程，來進行更為貼切的房價過程，並且詳加討論年金在不同情況下的變動，其中還考慮了借款人之死亡率是透過Gompertz-Makeham的死力法則來推估未來的死亡機率，以便於求取較適當的年金金額，來達到互惠雙方以增進社會福利的效果。 最後的研究結果表示，年金的支付金額會隨著借款人年齡越高而越多，也隨著房價上揚而提昇，顯示了房價服從指數Levy過程得到這樣的結果，與實際上的趨勢是不謀而合的。[[abstract]]The purpose of this study is to price reverse mortgages and to discuss about the details of the major risk And in the study is assumed that housing prices under exponential Lévy processes instead of geometric Brownian motion Moreover the Gompertz-Makeham mortality law modeled for the borrower All of the above the paper is investigated to find more appropriate annuities and the result presents that the annuity payment increases with the borrowers' age or the growing house pric