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Computing continuous-time growth models with boundary conditions via wavelets

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Abstract

This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are given

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  • Vidal-Sanz, Jose M., 2004. "Computing continuous-time growth models with boundary conditions via wavelets," DEE - Working Papers. Business Economics. WB wb045619, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    • Handle: RePEc:cte:wbrepe:wb045619
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    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Goffe, William L, 1993. "A User's Guide to the Numerical Solution of Two-Point Boundary Value Problems Arising in Continuous Time Dynamic Economic Models," Computational Economics, Springer;Society for Computational Economics, vol. 6(3-4), pages 249-255, November.
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    4. Mercedes Esteban-Bravo, 2004. "Computing Equilibria in General Equilibrium Models via Interior-point Methods," Computational Economics, Springer;Society for Computational Economics, vol. 23(2), pages 147-171, March.
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    6. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    7. Santos, Manuel S., 1999. "Numerical solution of dynamic economic models," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 5, pages 311-386, Elsevier.
    8. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    9. P. K. Venkatesh, 2001. "On the Optimum Control of Differential-Algebraic Equations," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 675-689, June.
    10. Nualart, David & Pardoux, Etienne, 1991. "Second order stochastic differential equations with Dirichlet boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 1-24, October.
    11. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    12. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729, Elsevier.
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    1. Avagyan, Vardan & Esteban-Bravo, Mercedes & Vidal-Sanz, Jose M., 2016. "Riding successive product diffusion waves. Building a tsunami via upgrade-rebate programs," International Journal of Research in Marketing, Elsevier, vol. 33(4), pages 780-796.
    2. Liu, Xiaoquan & Cao, Yi & Ma, Chenghu & Shen, Liya, 2019. "Wavelet-based option pricing: An empirical study," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1132-1142.
    3. repec:wyi:journl:002092 is not listed on IDEAS
    4. Chen Yi-Ting & Sun Edward W. & Yu Min-Teh, 2015. "Improving model performance with the integrated wavelet denoising method," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(4), pages 445-467, September.
    5. Avagyan, Vardan & Esteban-Bravo, Mercedes & Vidal-Sanz, Jose M., 2014. "Licensing radical product innovations to speed up the diffusion," European Journal of Operational Research, Elsevier, vol. 239(2), pages 542-555.
    6. repec:wyi:journl:002097 is not listed on IDEAS
    7. Haven, Emmanuel & Liu, Xiaoquan & Ma, Chenghu & Shen, Liya, 2009. "Revealing the implied risk-neutral MGF from options: The wavelet method," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 692-709, March.

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