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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。
Studied the family optimal consumption, life insurance purchase and portfolio selection in continuous time. Suppose that the family can invest in a risk-free asset and a risk asset, in which the expected excess return of the risk asset obeys the OU process of average return and in addition, it also gains human wealth - random labor income and life insurance purchase can hedge the family Loss of human fortune caused by accidental death of workers. According to the convex duality theory, Legendre transformation is used to find the explicit solution under the CARA utility function. The study finds that the purchase of family life insurance is a convex quadratic function of expected excess returns of risky assets and an increasing function of its volatility. As the excess returns increase, the value of wealth invested in risky assets gradually increases.