Optimal Investment and Consumption Decision of Family with Life Insurance

Posted: 16 Jun 2009 Last revised: 29 Oct 2010

See all articles by Minsuk Kwak

Minsuk Kwak

Department of Mathematics, Hankuk University of Foreign Studies

Yong Hyun Shin

Department of Mathematics, Sookmyung Women's University

U. Jin Choi

Korea Advanced Institute of Science and Technology (KAIST)

Date Written: June 15, 2009

Abstract

We study an optimal portfolio and consumption choice problem of family that combines life insurance of parents who receive deterministic labor income until the fixed time T. We consider utility functions of parents and children separately and assume that parents have uncertain lifetime. If parents die before the time 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 functions 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 changes of weight and other parameters such as lower bound of consumption, hazard rate affect the optimal policies.

Keywords: Life insurance, Optimal investment/consumption, Labor income, Utility maximization, Martingale method

JEL Classification: D91, E21, G11, G22

Suggested Citation

Kwak, Minsuk and Shin, Yong Hyun and Choi, U Jin, Optimal Investment and Consumption Decision of Family with Life Insurance (June 15, 2009). Available at SSRN: https://ssrn.com/abstract=1420487

Minsuk Kwak (Contact Author)

Department of Mathematics, Hankuk University of Foreign Studies ( email )

81 Oedae-ro
Yongin, 449-791
Korea, Republic of (South Korea)

Yong Hyun Shin

Department of Mathematics, Sookmyung Women's University ( email )

Cheongpa-ro 47-gil 100
Yongsan-Gu
Seoul, 04310
Korea, Republic of (South Korea)
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HOME PAGE: http://sites.google.com/site/yonghyunshin1972/

U Jin Choi

Korea Advanced Institute of Science and Technology (KAIST) ( email )

373-1 Kusong-dong
Yuson-gu
Taejon 305-701, 130-722
Korea, Republic of (South Korea)

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