Nisha Peng | Searcharxiv

arXiv2026

Faithful Decoding

This paper studies transformations that increase efficiency in solving equilibrium systems without information loss. Our approach exploits order-theoretic structure commonly found in economic problems to obtain conditions under which high-dimensional systems can be transformed into low-dimensional systems while preserving exact relationships between their solutions. The transformations can also be used for purposes other than dimensionality reduction, such as simplifying analysis and facilitating stochastic approximation routines. The theoretical ideas are illustrated using applications from economics and finance. In a real option problem, we demonstrate speed gains of up to 70,000 times.

econ.GN↗

arXiv2025

Dynamic Programming in Ordered Vector Space

New approaches to the theory of dynamic programming view dynamic programs as families of policy operators acting on partially ordered sets. In this paper, we extend these ideas by shifting from arbitrary partially ordered sets to ordered vector spaces. The integrated algebraic and order structure in such spaces leads to sharper fixed point results. These fixed point results can then be exploited to obtain optimality properties. We illustrate our results through applications ranging from firm management to data valuation. These applications include features from the recent literature on dynamic programming, including risk-sensitive preferences, nonlinear discounting, and state-dependent discounting. In all cases we establish existence of optimal policies, characterize them in terms of Bellman optimality relationships, and prove convergence of major algorithms.

math.OC↗