Research

My work covers the theory of dynamic programming and its applications in economics and finance. In particular, some of my work focuses on the existence and uniqueness of equilibria under nonstandard discounting conditions. I’m also interested in the computation of asset pricing models as well as functional equations in general.

Working Papers

• Unique Solutions to Power-Transformed Affine Systems with John Stachurski and Ole Wilms   

  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.

Publications

• Asset pricing with time preference shocks: Existence and uniqueness with John Stachurski and Ole Wilms   
  Journal of Economic Theory 216 (2024): 105781

  This paper studies existence and uniqueness of recursive utility in asset pricing models with time preference shocks. We provide conditions that clarify existence and uniqueness for a wide range of models, including exact necessary and sufficient conditions for standard formulations. The conditions isolate the roles of preference parameters, as well as the different risks that drive the consumption and preference shock processes. By deriving and decomposing a stability coefficient for recursive utility models, we show how different parameters in the model interact to determine existence and uniqueness of solutions.

• Coase Meets Bellman: Dynamic Programming for Production Networks with Tomoo Kikuchi, Kazuo Nishimura, and John Stachurski      
  Journal of Economic Theory 196 (2021): 105287

  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.

• Dynamic Programming with State-Dependent Discounting with John Stachurski      
  Journal of Economic Theory 192 (2021): 105190

  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.

• Equilibrium in Production Chains with Multiple Upstream Partners with Meng Yu         
  Journal of Mathematical Economics 83 (2019): 1-10

  In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence improving their results on production networks with multiple upstream partners. We propose an algorithm for computing the equilibrium price function that is more than ten times faster than successive evaluations of the operator. The model is then generalized to a stochastic setting that offers richer implications for the distribution of firms in a production network.

• The Substitution and Pervasiveness Effects of ICT on China’s Economic Growth (in Chinese) with Yuezhou Cai
  经济研究 / Economic Research Journal 12 (2015): 100-114