<?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;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">895</style></section></record><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%">JINGXIAO ZHANG</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%">FAIR PRICING OF REVERSE MORTGAGE WITHOUT REDEMPTION RIGHT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">25</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We derive in this article the pricing of a reverse mortgage without redemption right. In this, the underlying model employs a jump-diffusion process to represent the dynamics of the housing price, the Vasicek model to drive the instantaneous interest rate, and the force mortality model to describe the longevity risk. The said pricing is based on the Principle of Balance between the expected gain and expected payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. We also present, with the above model, explicit formulas for the increasing (or decreasing) perpetual annuity and the level perpetual annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters associated with the house price, the interest rate, and the force of mortality model. Finally, some numerical results for the lump sum, the annuity, and the annuity payment factors are presented, and also the sensitivity with respect to the above parameters is discussed. Based on the average change rate, we evaluate all parameters’ degree of impact on the annuity, the lump sum, and the annuity payment factors.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">473</style></section></record><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%">JINGXIAO ZHANG</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%">PRICING AN INSURANCE PRODUCT THAT INTEGRATES REVERSE MORTGAGE WITH LONG-TERM CARE INSURANCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">25</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We derive in this article the pricing formula for an insurance product that integrates reverse mortgage with long term care. This pricing is based on the principle of balance between the mean gain and mean payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. Here, we assume that the dynamics of the housing price is driven by the Black-Scholes model and the interest rate is driven by the Ornstein-Uhlenbeck process. With these assumptions, we present closed-form formulas for the growing perpetuity annuity, the state annuity, and the constant annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters of housing price, interest rate model, and the age of the insured. We present the numerical results for the lump sum, the annuity, and the annuity payment factors, and analyze the sensitivity with respect to the above parameters. We also show that the mean return of housing price has the dominating influence on the lump sum and annuity&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">11</style></section></record><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%">ZHANG JINGXIAO</style></author><author><style face="normal" font="default" size="100%">CAO KAI</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%">OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT IN JUMP DIFFUSION MARKETS WITH NO SHORT-SELLING AND NO BORROWING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/13-dsa-169-186.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The optimal reinsurance and investment problem for insurance has attracted a lot of attention of researchers in the field of stochastic control for a long time. Along this line we discuss this problem in the case of jump diffusion markets when neither short-selling nor borrowing is allowed. Here, we specifically assume that the risk process of the insurance company is a diffusion process. The insurance company can transfer its risk by reinsurance and also invest its surplus in the financial market, where we model the price of the risky asset by a geometric L´evy process. To maximize the CARA (Constant Absolute Risk Aversion) utility of terminal wealth, the HJB equation with no short-selling constraint has been considered, and we obtain the closed form of the value function by a standard method. However, only a handful of people have discussed this problem under both constraints, (i.e. no short-selling and no borrowing). This is because the problem is much more general in this context, and becomes so complex that analytical solution could hardly be obtained. Therefore, we provide, under the no short-selling and no borrowing constraints, a numerical solution via Markov chain approximation, which proves to be effective and amenable.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">169</style></section></record><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%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</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%">OPTIMAL DIVIDEND AND REINSURANCE UNDER THRESHOLD STRATEGY</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%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/14-DSA-31-07.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider the optimal dividend and reinsurance problems in this article, where the dividend strategy is the threshold strategy and the reinsurance is the proportional reinsurance. Despite the fact that the barrier strategy has its popularity in theoretical research, such a strategy has little practical acceptance as it will lead to the certainty of ultimate ruin. A modified version of the barrier strategy is the threshold strategy which assumes that dividends are paid at a rate smaller than the rate of premium income whenever the surplus is above some threshold level, and that no dividends are paid out whenever the surplus is below the threshold level. In this article, we consider two cases of the threshold strategy. One is the threshold strategy without barrier, and the other is the threshold strategy with barrier. The first case generalizes and corrects part of results in [16]. In the second case, we use the stochastic control theoretic techniques, to find the value function as well as the optimal investment-reinsurance policy in closed form.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">193</style></section></record><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%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</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%">OPTIMAL DIVIDEND PROBLEM WITH THE INFLUENCE OF DIVIDEND PAYOUTS ON INSURANCE BUSINESS</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%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/34-DSA-31-21.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article initiates the optimal dividend problem, from the view point of the managers of the insurance companies. where we incorporate the influence of dividend payouts on the insurance business. We begin with a mathematical characterization of the influence of dividend payouts, and then continue to find the optimal dividend policy that maximizes the expected utility of terminal wealth and minimizes the ruin probability. We study the problem in terms of the Levy process and derive the diffusion process case as a particular one.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">519</style></section></record><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%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</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%">OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE UNDER NO SHORT-SELLING AND NO BORROWING</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%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/15-DSA-31-10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Insurance companies resort to investment and reinsurance, among other options, to manage their reseerves. This article addresses the problem of optimal investment and reinsurance when no short-selling and no borrowing allowed. More specifically, we assume that the risk process of the insurance company is a compound Poisson process perturbed by a standard Brownian motion and that the risk can be reduced through a proportional reinsurance. In addition, the surplus can be invested in the financial market such that the portfolio will consist, for simplicity, of one risky asset and one risk-free asset. Our goal is to find the optimal investment and reinsurance policy which can maximize the expected exponential utility of the terminal wealth. In the case of no short-selling, we find the closed form of value function as well as the optimal investment-reinsurance policy. In the case when neither short-selling nor borrowing allowed, the resulting HJB equation is difficult to solve analytically, and hence we provide a numerical solution through Markov chain approximation techniques&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">205</style></section></record><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%">BO ZHANG</style></author><author><style face="normal" font="default" size="100%">JING XU</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%">A BACKWARDS STOCHASTIC DIFFERENTIAL EQUATION MODEL IN LIFE INSURANCE</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%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/327-336-DSA-26-16-ZhangXuKannan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article we obtain the ratio of risk investment and the optimal accumulated level of single premium endowment insurance in the case of dynamic investment strategies of life insurance company by BSDEs. It gives an illustration of traditional reserve valuation, and prudential rules.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">327</style></section></record></records></xml>