CAJ | 학술논문

本文在随机寿命和随机金融资产收益率的假定下，利用必要财富增长率来度量退休人员的财富短缺风险，即在给定的个人财富过程和给定的置信度（95％）下，在给定的时间段内（死亡时刻之前），使财富值保持为正的最低财富增长率。本文利用随机死亡率模型和退休人员财富变化过程推导退休人员的财富短缺概率，并利用数值算法求解财富短缺概率低于5％时的财富必要收益率。最后，本文从消费的角度划分了三类老年群体：基准群体、遗赠群体和独居群体，比较这三类群体的财富短缺风险特征；之后进行参数敏感性分析，认为消费物价指数和国债收益波动率的增大均加大了老年人的财富短缺风险。本文对必要财富收益率的度量为将来设计多样化养老金融产品的收益率提供了参考标尺。
본문재수궤수명화수궤금융자산수익솔적가정하，이용필요재부증장솔래도량퇴휴인원적재부단결풍험，즉재급정적개인재부과정화급정적치신도（95％）하，재급정적시간단내（사망시각지전），사재부치보지위정적최저재부증장솔。본문이용수궤사망솔모형화퇴휴인원재부변화과정추도퇴휴인원적재부단결개솔，병이용수치산법구해재부단결개솔저우5％시적재부필요수익솔。최후，본문종소비적각도화분료삼류노년군체：기준군체、유증군체화독거군체，비교저삼류군체적재부단결풍험특정；지후진행삼수민감성분석，인위소비물개지수화국채수익파동솔적증대균가대료노년인적재부단결풍험。본문대필요재부수익솔적도량위장래설계다양화양로금융산품적수익솔제공료삼고표척。
Under the assumption of the stochastic life expectancy and random yield of financial assets, we use the necessary wealth growth rate as a measure of the retirees＇ wealth shortfall risk. The necessary wealth growth rate is the lowest wealth growth rate that, in the given process of personal wealth and under the given confidence level （95 % ）, during the given time period （before death moment）, that makes the personal wealth keep positive. Using stochastic mortality model and personal wealth process, we deduce retirees＇ wealth shortfall probability, and then use the numerical algorithm to calculate the necessary wealth growth rate when the wealth shortfall probability is lower than 5%. Finally, from the perspective of consumption, we divide the old into three groups： the basic group, the bequest group, and the lonely group; then, we compare the characteristics of the wealth shortfall risk among three elderly groups. After the sensitiveness analysis of parameters, we find that CPI and volatility of government bonds exacerbate retirees＇ wealth shortfall risk. Our work figures out the necessary wealth growth rate, and provide references for setting yields of pension financial products.