Dynamic Programming with State-Dependent Discounting

TL;DR

This paper extends dynamic programming theory to include state-dependent discounting, providing conditions for standard optimality results to hold, applicable to complex economic models with recursive preferences.

Contribution

It introduces a general framework for state-dependent discounting in dynamic programming, ensuring the validity of key optimality results under broad conditions.

Findings

Established a condition on the discount factor process for optimality results

Demonstrated the condition cannot be significantly weakened

Applicable to models with recursive preferences and unbounded rewards

Abstract

This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results can be recovered. We also show that the condition cannot be significantly weakened. Our framework is general enough to handle complications such as recursive preferences and unbounded rewards. Economic and financial applications are discussed.