CAJ | 학술논문

研究了连续时间下家庭最优消费、人寿保险购买与投资组合选择。假定家庭可投资于一种无风险资产和一种风险资产，其中风险资产的预期超额收益服从均值回复的O-U过程，此外，还会获得人力财富---随机劳动收入，人寿保险的购买可以对冲家庭劳动者意外死亡带来的人力财富损失。根据凸对偶理论利用Legendre 转换求出了CARA效用函数下的显式解。研究发现家庭人寿保险购买是风险资产预期超额收益的凸二次函数，是其波动率的增函数，随着超额收益的增加投资于风险资产上的财富值逐渐增加。
연구료련속시간하가정최우소비、인수보험구매여투자조합선택。가정가정가투자우일충무풍험자산화일충풍험자산，기중풍험자산적예기초액수익복종균치회복적O-U과정，차외，환회획득인력재부---수궤노동수입，인수보험적구매가이대충가정노동자의외사망대래적인력재부손실。근거철대우이론이용Legendre 전환구출료CARA효용함수하적현식해。연구발현가정인수보험구매시풍험자산예기초액수익적철이차함수，시기파동솔적증함수，수착초액수익적증가투자우풍험자산상적재부치축점증가。
This paper studies an optimal household consumption , life insurance and portfolio choice in a contin-uous time framework .The household is not only allowed to invest in a risk -free asset and a risky asset , but also obtain human capital .The expected excess return rate of the risky asset is driven by mean -reverting process , which can reflect the states of the market .Life insurance can be purchased to hedge the loss of human wealth due to the accidental death caused by breadwinner .By applying the convex dual theory and Legendre transform , the ex-plicit solutions are obtained by employing CARA utility function .We show that life insurance is a convex quadratic function of expected excess return rate , increases when the volatility becomes larger , meanwhile , the wealth inves-ted in the risky asset increases when the excess return rate becomes larger .