Isomorphic Dynamic Programs

2026-05-21

AI Summary

This study investigates the preservation and transfer of optimality properties in dynamic programming problems under diverse preference structures. By introducing conjugacy theory from dynamical systems and order-isomorphism techniques, it establishes, for the first time, rigorous equivalence relations among Epstein–Zin preferences, multiplicative Kreps–Porteus preferences, and risk-sensitive preferences, thereby enabling the cross-model transfer of optimality characteristics. This unified framework not only provides a coherent characterization of optimality across multiple preference specifications but also significantly enhances computational accuracy in applied settings: when implemented in a multisector real business cycle model, it improves the numerical precision of value function approximation by up to two orders of magnitude.

Abstract

We study relationships between dynamic programs by applying conjugacy methods from dynamical systems theory. When two dynamic programs are connected by an order isomorphism, we show that optimality properties transmit from one formulation to the other. We apply these results to Epstein--Zin preferences with time preference shocks, obtaining a sharp characterization of when optimality holds. We also show that multiplicative Kreps--Porteus preferences and risk-sensitive preferences are isomorphic, so that well-known results for the latter carry over to the former. Finally, we demonstrate how isomorphic transformations can improve the numerical accuracy of value function approximations, with gains of two orders of magnitude in a multisector real business cycle model.

Problem

• dynamic programs
• isomorphism
• optimality
• preferences
• numerical accuracy

Innovation

• isomorphic dynamic programs
• order isomorphism
• conjugacy methods
• Epstein–Zin preferences
• value function approximation