Aoki, Takaaki
(2013):
*Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics.*

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## Abstract

This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. We analyzed the special case where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. We show that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions with distinct steady states (indeterminacy of self-consistent policy functions).

Item Type: | MPRA Paper |
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Original Title: | Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics |

English Title: | Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics |

Language: | English |

Keywords: | Bellman equation, Two-sided altruism, Dynamic inconsistency, Self-consistent policy functions, Indeterminacy, Overlapping generations model. |

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis D - Microeconomics > D9 - Intertemporal Choice > D91 - Intertemporal Household Choice ; Life Cycle Models and Saving O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models |

Item ID: | 44994 |

Depositing User: | Takaaki Aoki |

Date Deposited: | 01 Aug 2013 15:21 |

Last Modified: | 07 Oct 2019 17:37 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/44994 |