## Abstract

Recursive utility disentangles preferences with respect to time and risk by recursively building up a value function of local increments. This involves certainty equivalents of indirect utility. Instead we disentangle preferences with respect to time and risk by building up a value function as a non-linear aggregation of certainty equivalents of direct utility of consumption. This entails time-consistency issues which are dealt with by looking for an equilibrium control and an equilibrium value function rather than a classical optimal control and a classical optimal value function. We characterize the solution in a general diffusive incomplete market model and find that, in certain special cases of utmost interest, the characterization coincides with what would arise from a recursive utility approach. But also importantly, in other cases, it does not: The two approaches are fundamentally different but match, exclusively but importantly, in the mathematically special case of homogeneity of the value function.

Original language | English |
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Pages (from-to) | 95-108 |

Number of pages | 14 |

Journal | Journal of Mathematical Economics |

Volume | 90 |

Early online date | 16 Jul 2020 |

DOIs | |

Publication status | Published - Oct 2020 |

## Keywords

- Certainty equivalents
- Equilibrium strategies
- Generalized Hamilton–Jacobi–Bellman equation
- Recursive utility
- Time-consistency
- Time-global preferences

## ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics