<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LINA MA</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">VALUATION OF REVERSE MORTGAGE WITH DEPENDENT JOINT LIVES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">joint annuity</style></keyword><keyword><style  face="normal" font="default" size="100%">jump-diffusion</style></keyword><keyword><style  face="normal" font="default" size="100%">lifetime model</style></keyword><keyword><style  face="normal" font="default" size="100%">reverse mortgage</style></keyword><keyword><style  face="normal" font="default" size="100%">valuation</style></keyword><keyword><style  face="normal" font="default" size="100%">Vasicek model</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">12/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">32</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Utilizing the principle of balance between expected gain and expected&amp;nbsp;payment, this work obtains the analytic valuation formula for reverse mortgage. In&amp;nbsp;particular, we provide the formulas for the lump sum payment, joint annuity, increasing (decreasing) annuity, and level annuity of reverse mortgage. We also derive the&amp;nbsp;valuation equation that the variable payment annuities satisfy. We then discuss the&amp;nbsp;monotonicity of the lump sum, annuity, and annuity payment factors with respect to&amp;nbsp;the parameters associated with the home price and the interest rate model. Finally,&amp;nbsp;we analyze the sensitivity of the joint annuity with respect to the parameters associated with the home price, interest rate, and lifetime model. The numerical results&amp;nbsp;show that the average return of home price exerts a dominating influence on the joint&amp;nbsp;annuity, followed by the mean reversion level of interest rate, and both of them have&amp;nbsp;stronger impact on the annuities of younger applicants than those of older applicants.&amp;nbsp;Meanwhile, the initial age of male and that of female produce asymmetrical effect&amp;nbsp;on the joint annuity. Remarkably, the dependence of joint-lifetime significantly affect&amp;nbsp;the joint annuity value. In case that the male and female initial ages are both less&amp;nbsp;than 80 years old, annuity values on average increase&amp;nbsp; approximately 4.5%, and the&amp;nbsp;greatest increment of annuity value approaches 9%.&lt;/p&gt;
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