Existence and Uniqueness of Solutions to the Stochastic Bellman Equation with Unbounded Shock

2019-07-17

In this paper we develop a general framework to analyze stochastic dynamic problems with unbounded utility functions and correlated and unbounded shocks. We obtain new results of the existence and uniqueness of solutions to the Bellman equation through a general fixed point theorem that generalizes known results for Banach contractions and local contractions. We study an endogenous growth model as well as the Lucas asset pricing model in an exchange economy, significantly expanding their range of applicability.

📄 PDF Abstract BibTeX arXiv:1907.07343

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On solutions of the distributional Bellman equation

2022-01-31 · Julian Gerstenberg, Ralph Neininger, Denis Spiegel

In distributional reinforcement learning not only expected returns but the complete return distributions of a policy are taken into account. The return distribution for a fixed policy is given as the solution of an assoc…

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Deep Reinforcement Learning

Existence and Uniqueness of Solutions to the Stochastic Bellman Equation with Unbounded Shock

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