住房反向抵押贷款主体行为策略选择——基于演化博弈模型分析

On the Behavioral Strategy Selection of the Housing Reverse Mortgage:An Analysis Based on Evolutionary Game Model

构建包含老年人、金融机构和政府部门在内的三方演化博弈模型,采用MATLAB 2021a进行数值仿真,分析住房反向抵押贷款各种策略的有效性。研究表明:当老年人申请住房反向抵押贷款的消费效用大于将房产遗赠给子女获得的遗赠效用和消费养老储蓄所获得的消费效用总和时,住房反向抵押贷款市场有且仅有(申请、开展、支持)一种演化均衡状态;其他博弈参与者选择住房反向抵押贷款的概率越高,某一博弈参与者选择住房反向抵押贷款的概率也会随之升高;住房反向抵押贷款市场的初始状态和博弈支付矩阵的相关参数会对市场的整体演化产生影响。具体表现为房价越高,住房反向抵押贷款市场演化至(申请、开展、支持)均衡点的速度越快,与遗产税税率的影响截然相反。

A tripartite evolutionary game model including the elderly,financial institutions and government de⁃partments is constructed,and numerical simulation is performed using MATLAB 2021a to analyze the effective⁃ness of various strategies of the housing reverse mortgage.The study shows:there is one and only one evolu⁃tionary equilibrium in the reverse mortgage market(application,implementation and support)when the con⁃sumption utility of the elderly applying for a reverse mortgage is greater than the sum of the legacy utility ob⁃tained by bequeathing the property to their children and the consumption utility gained from consuming their re⁃tirement savings;the higher the probability of other game participants choosing reverse mortgages,the higher the probability of a given game participant choosing a reverse mortgage;the initial state of the housing reverse mort⁃gage market and the relevant parameters of the game payment matrix have an impact on the overall evolution of the market.This is shown by the fact that the higher the house price,the faster the housing reverse mortgage market evolves to the equilibrium point of(application,implementation and support),which is diametrically op⁃posed to the effect of the estate tax rate.