Computational Economics

, Volume 42, Issue 2, pp 175–198 | Cite as

Tensor Spline Approximation in Economic Dynamics with Uncertainties

  • Moody T. ChuEmail author
  • Chun-Hung Kuo
  • Matthew M. Lin


Modern economic theory views the economy as a dynamical system in which rational decisions are made in the face of uncertainties. Optimizing decisions over time on market behavior such as consumption, investment, labor supply, and technology innovation is of practical importance. Interpreting all market behavior in a broad sense, the problem finds further applications in many areas other than economics. Finding the policy function inherent in the associated Euler equation has been an important but challenging task. This note proposes using composite 1-dimensional cubic splines in tensor form to process the Newton iterative scheme on approximating the unknown policy functions. This tensor spline approach has the advantages of freedom in the node collocation, simplicity in the derivative calculation, fast convergence, and high precision over the conventional projection methods. Applications to the neoclassical growth model with leisure choice are used to demonstrate the working of the idea. In particular, tensor products are employed throughout to simplify and effectuate the operations.


Economic dynamics Dynamic programming Stochastic uncertainties Bellman equation Euler equation Policy function Cubic spline Tensor operation 

Mathematics Subject Classification

37B35 37N40 90C22 90C51 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of EconomicsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of MathematicsNational Chung Cheng UniversityChia-YiTaiwan

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