arXiv subjects

John Stachurski

Publications and source records attributed to John Stachurski.

At least 19 recordsLinked to original sources

arXiv2026

A New Approach to Goodness of Fit for Ergodic Markov Processes

We introduce a new density-based goodness of fit test for ergodic Markov processes. Our test compares the data against the class of models specified in the null hypothesis, and rejects if no model in the class yields a stationary density that matches with the data. No alternative needs to be specified in order to implement the test. Although our test compares densities, estimation of smoothing parameters is not required, and the test has nontrivial power against $1/\sqrt{n}$ local alternatives. The test provides new perspectives on some existing problems in econometric and financial modeling.

stat.ME↗

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↗

arXiv2026

Abstract Dynamic Programming on Partially Ordered Spaces

We study abstract dynamic programs on partially ordered spaces, pairing the order-theoretic approach to dynamic programming with topological and metric foundations. We show that readily verifiable forms of topological stability, such as global stability and contractivity of the policy operators, deliver the fundamental optimality properties of dynamic programming together with convergence of value function iteration, Howard policy iteration, and optimistic policy iteration. We also prove that stationary policies dominate nonstationary policy plans under very weak assumptions. Applications include Markov decision processes, structural estimation problems in which maximization and integration are interchanged, optimal stopping without discounting, and Bayesian sequential analysis. For the last two, our results weaken existing assumptions and extend algorithmic guarantees for foundational problems.

math.OC↗

arXiv2026

Isomorphic Dynamic Programs

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.

econ.GN↗

arXiv2026

Stationary Distributions in Monotone Markov Models: Theory and Applications

Many economic models feature monotone Markov dynamics on state spaces that may be noncompact. Establishing existence, uniqueness, and stability of stationary distributions in such settings has required a patchwork of sufficient conditions, each tailored to specific applications. We provide a single necessary and sufficient condition: a monotone Markov process has a globally stable stationary distribution if and only if it is asymptotically contractive and has a tight trajectory. This characterization covers both compact and noncompact state spaces, discrete and continuous time, and extends to nonlinear Markov operators that depend on aggregate state. We demonstrate the result through applications to wage dynamics, Bayesian learning with belief shocks, and income processes that generate Pareto tails.

math.PR↗

arXiv2026

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↗

arXiv2025

Dynamic Programming: From Local Optimality to Global Optimality

In the theory of dynamic programming, an optimal policy is a policy whose lifetime value dominates that of all other policies from every possible initial condition in the state space. This raises a natural question: when does optimality from a single state imply optimality from every state? Working in a general setting, we provide sufficient conditions for this property that relate to reachability and irreducibility. Our results have significant implications for modern policy-based algorithms used to solve large-scale dynamic programs. We illustrate our findings by applying them to an optimal savings problem via an algorithm that implements gradient ascent in a policy space constructed from neural networks.

math.OC↗

arXiv2025

Dynamic Programs on Partially Ordered Sets

We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all subfields of dynamic programming fit into this framework. These range from traditional dynamic programs to those involving nonlinear recursive preferences, desire for robustness, function approximation, Monte Carlo sampling and distributional dynamic programs. We apply the framework to establish new optimality and algorithmic results for specific applications.

math.OC↗

arXiv2024

A Unified Stability Theory for Classical and Monotone Markov Chains

This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel probability measures based on partial stochastic dominance. We then show that many conventional results framed in the setting of total variation distance have natural generalizations to the partially ordered setting when this metric is adopted.

math.PR↗

arXiv2024

Quantitative Convergence Rates for Stochastically Monotone Markov Chains

For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic mixing conditions. We complement these results by providing quantitative bounds on deviations between distributions. We also show that well-known total variation bounds can be recovered as a special case.

math.PR↗

arXiv2024

Partial Stochastic Dominance via Optimal Transport

In recent years, a range of measures of partial stochastic dominance have been introduced. These measures attempt to determine the extent to which one distribution is dominated by another. We assess these measures from intuitive, axiomatic, computational and statistical perspectives. Our investigation leads us to recommend a measure related to optimal transport as a natural default.

math.PR↗

arXiv2024

Interest Rate Dynamics and Commodity Prices

In economic studies and popular media, interest rates are routinely cited as a major factor behind commodity price fluctuations. At the same time, the transmission channels are far from transparent, leading to long-running debates on the sign and magnitude of interest rate effects. Purely empirical studies struggle to address these issues because of the complex interactions between interest rates, prices, supply changes, and aggregate demand. To move this debate to a solid footing, we extend the competitive storage model to include stochastically evolving interest rates. We establish general conditions for existence and uniqueness of solutions and provide a systematic theoretical and quantitative analysis of the interactions between interest rates and prices.

econ.TH↗

arXiv2024

Firm Entry and Exit with Unbounded Productivity Growth

In Hopenhayn's (1992) entry-exit model productivity is bounded, implying that the predicted firm size distribution cannot match the power law tail observable in the data. In this paper we remove the boundedness assumption and, in this more general setting, provide an exact characterization of existence of stationary equilibria, as well as a novel sufficient condition for existence based on treating production as a Lyapunov function. We also provide new representations of the rate of entry and aggregate supply. Finally, we prove that the firm size distribution has a power law tail under a very broad set of productivity growth specifications.

econ.GN↗

arXiv2024

Dynamic Programming: Finite States

This book is about dynamic programming and its applications in economics, finance, and adjacent fields. It brings together recent innovations in the theory of dynamic programming and provides applications and code that can help readers approach the research frontier. The book is aimed at graduate students and researchers, although most chapters are accessible to undergraduate students with solid quantitative backgrounds.

econ.GN↗

arXiv2022

Unique Solutions to Power-Transformed Affine Systems

Systems of the form $x = (A x^s)^{1/s} + b$ arise in a range of economic, financial and control problems, where $A$ is a linear operator acting on a space of real-valued functions (or vectors) and $s$ is a nonzero real value. In these applications, attention is focused on positive solutions. We provide a simple and complete characterization of existence and uniqueness of positive solutions under conditions on $A$ and $b$ that imply positivity.

math.FA↗

arXiv2022

Economic Networks: Theory and Computation

This textbook is an introduction to economic networks, intended for students and researchers in the fields of economics and applied mathematics. The textbook emphasizes quantitative modeling, with the main underlying tools being graph theory, linear algebra, fixed point theory and programming. The text is suitable for a one-semester course, taught either to advanced undergraduate students who are comfortable with linear algebra or to beginning graduate students.

econ.GN↗

arXiv2022

Systemic Risk in Financial Systems: Properties of Equilibria

Eisenberg and Noe (2001) analyze systemic risk for financial institutions linked by a network of liabilities. They show that the solution to their model is unique when the financial system is satisfies a regularity condition involving risk orbits. We show that this condition is not needed: a unique solution always exists.

q-fin.MF↗

arXiv2021

Coase Meets Bellman: Dynamic Programming for Production Networks

We show that competitive equilibria in a range of models related to production networks can be recovered as solutions to dynamic programs. Although these programs fail to be contractive, we prove that they are tractable. As an illustration, we treat Coase's theory of the firm, equilibria in production chains with transaction costs, and equilibria in production networks with multiple partners. We then show how the same techniques extend to other equilibrium and decision problems, such as the distribution of management layers within firms and the spatial distribution of cities.

econ.GN↗