Optimal Investment and Consumption Decision of Family with Life Insurance

We study an optimal portfolio and consumption choice problem of family that combines life insurance of parents who receive deterministic labor income until fixed time horizon T . We consider utility functions of parents and children separately and assumed that parents have uncertain lifetime. If parents die before T , children have no income and they choose the optimal consumption and portfolio with remaining wealth combining the insurance benefit. Before the death time of parents, the object of family is to maximize weighted average of utility of parents and children. It is assumed that the utility function of both parents and children belong to HARA utility class. Using HARA utility we impose the condition that instantaneous consumption rate should be above a given lower bound. We analyze how the change of weight and other parameters such as lower bound of consumption, income process, hazard rate affect the optimal policies using various numerical examples. ∗We are grateful to Hyeng Keun Koo and Jaeyoung Sung for useful comments and advice. †Department of Mathematical Science, KAIST, Daejeon 305701, Republic of Korea, E-mail address: [email protected], Corresponding author. This work was partially supported by BK21 project of Department of Mathematical Science, KAIST and the KRF grant funded by the Korea Government(MEST) (Grant No. 2009-0072021). ‡School of Computational Sciences, Korea Institute for Advanced Study (KIAS), Seoul 130722, Republic of Korea. This work was supported by the KRF grant funded by the Korea Government(MEST) (Grant No. 2009-0072021). §Department of Mathematical Science, KAIST, Daejeon 305701, Republic of Korea. This work was supported by BK21 project of Department of Mathematical Science, KAIST.