## Abstract

This paper investigates a consumption-leisure-investment problem, where the object of an economic agent is to maximize the expected value of discounted lifetime utility in a life-cycle model. The agent is allowed to have considerable labor flexibility and the date of retirement is fixed. To incorporate some well-documented behavioral features of human beings, we consider the situation where the discounting is non-exponential. This situation is far from trivial and renders the optimization problem of the agent to be a nonstandard one, namely, a time-inconsistent stochastic control problem. The extended HJB equation for the time-inconsistent control problem is given. A verification theorem is proved for a general discount function and a general utility function. Explicit-form solutions are presented for the logarithmic utility with exponential discounting, pseudo-exponential discounting and hyperbolic discounting.

Original language | English |
---|---|

Pages (from-to) | 6057-6079 |

Number of pages | 23 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 49 |

Issue number | 24 |

DOIs | |

Publication status | Published - 16 Dec 2020 |

## Keywords

- Labor flexibility
- life-cycle model
- non-exponential discounting
- time-inconsistence
- equilibrium strategies
- extended HJB equation