We study optimal portfolio, consumption-leisure and retirement choice of an infinitely lived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution (CES) function of consumption and leisure. We integrate in one model the optimal consumption-leisure-work choice, the optimal portfolio selection, and the optimal stopping problem in which the agent chooses her retirement time. The economic agent derives utility from both consumption and leisure, and is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. We solve the problem analytically by considering a variational inequality arising from the dual functions of the optimal stopping problem. The optimal retirement time is characterized as the first time when her wealth exceeds a certain critical level. We provide the critical wealth level for retirement and characterize the optimal consumption-leisure and portfolio policies before and after retirement in closed forms. We also derive properties of the optimal policies. In particular, we show that consumption in general jumps around retirement.We are grateful to two anonymous referees and an associate editor for helpful comments and advice. We also appreciate Hyeng Keun Koo for helpful comments.Manuscript

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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.

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In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.

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