Skip to main content

Isotone Recursive Methods: The Case of Homogeneous Agents

  • Chapter

Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (Canada)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Abian, S. and A. B. Brown. 1962. A theorem on partially order sets with applications to fixed point theorems. Canadian Journal of Mathematics, 13, 78–82.

    MathSciNet  Google Scholar 

  2. Aiyagari, R. 1994. Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics, 109, 659–684.

    CrossRef  Google Scholar 

  3. Amann, H. 1976. Fixed equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review, 18, 620–709.

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. Amann, H. 1977. Order Structures and Fixed Points. SAFA 2, ATTI del 2. Seminario di Analisi Funzionale e Applicazioni. MS.

    Google Scholar 

  5. Amir, R. 1996. Sensitivity analysis of multisector optimal economic dynamics, Journal of Mathematical Economics, 25, 123–141.

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Amir, R., L. Mirman and W. Perkins. 1991, One-sector nonclassical optimal growth: optimality conditions and comparative dynamics. International Economic Review, 32, 625–644.

    MathSciNet  Google Scholar 

  7. Antoniadou, E. 1995. Lattice Programming and Economic Optimization. Ph.D. Dissertation. Stanford University.

    Google Scholar 

  8. Askri, K. and C. Le Van. 1998. Differentiability of the value function of nonclassical optimal growth models. Journal of Optimization Theory and Applications. 97, 591–604.

    CrossRef  MathSciNet  Google Scholar 

  9. Becker, R. and C. Foias. 1998. Implicit programming and the invariant manifold for Ramsey equilibria. in Y. Abramovich, E. Avgerinos, and N. Yannelis, eds. Functional Analysis and Economic Theory, 1998, Springer-Verlag.

    Google Scholar 

  10. Becker R, and I. Zilcha. 1997. Stationary Ramsey equilibria under uncertainty. Journal of Economic Theory, 75, 122–140.

    CrossRef  MathSciNet  Google Scholar 

  11. Berge, C. 1963. Topological Spaces, MacMillan Press.

    Google Scholar 

  12. Bewley, T. 1986. Stationary monetary equilibrium with a continuum of independently fluctuating consumers. in Contributions to Mathematics in Honor of Gerard Debreu, ed. W. Hildenbrand and A. Mas-Colell. North-Holland, Amsterdam.

    Google Scholar 

  13. Birkhoff, G. 1967. Lattice Theory. AMS Press.

    Google Scholar 

  14. Bizer, D. and K. Judd. 1989. Taxation and uncertainty. American Economic Review, 79, 331–336.

    Google Scholar 

  15. Bourbaki, N. 1950, Sur le Théorème de Zorn, Archiv der Mathematik, 2 (1949–1950), 434–437.

    CrossRef  MathSciNet  Google Scholar 

  16. Brock, W. and L. Mirman. 1972. Optimal growth and uncertainty: the discounted case. Journal of Economic Theory, 4, 479–513.

    CrossRef  MathSciNet  Google Scholar 

  17. Clarke, F. 1983. Optimization and Nonsmooth Analysis. SIAM Press.

    Google Scholar 

  18. Coleman, W. J. II. 1990. Solving the stochastic growth model by policyfunction iteration. Journal of Business and Economic Statistics, 8, 27–29.

    CrossRef  Google Scholar 

  19. Coleman, W. J., II. 1991. Equilibrium in a production economy with an income tax. Econometrica, 59, 1091–1104.

    MATH  MathSciNet  Google Scholar 

  20. Coleman, W. J., II. 1997. Equilibria in distorted infinite-horizon economies with capital and labor, Journal of Economic Theory, 72, 446–461.

    CrossRef  Google Scholar 

  21. Coleman, W. J., II. 2000. Uniqueness of an equilibrium in infinite-horizon economies subject to taxes and externalities, Journal of Economic Theory 95, 71–78.

    CrossRef  MATH  MathSciNet  Google Scholar 

  22. Datta, M., L. J. Mirman and K. L. Reffett. 2002. Existence and uniqueness of equilibrium in distorted dynamic economies with capital and labor Journal of Economic Theory, 103, 377–410.

    CrossRef  MathSciNet  Google Scholar 

  23. Datta, M., L. J. Mirman, O. F. Morand and K. L. Reffett. 2005. Markovian equilibrium in infinite horizon economies with many agents, incomplete markets and public policy. Journal of Mathematical Economics, 41, 505–544.

    CrossRef  MathSciNet  Google Scholar 

  24. Datta, M. and K. L. Reffett. 2005. Computing Markovian equilibrium in large economies I: Bewley models with no aggregate risk. MS, Arizona State University.

    Google Scholar 

  25. Davey, B. and H. Priestley. 2002. Introduction to Lattices and Order. Cambridge Press, 2nd edition.

    Google Scholar 

  26. Davis, A. 1955. A characterization of complete lattices. Pacific Journal of Mathematics, 5, 311–319.

    MATH  MathSciNet  Google Scholar 

  27. Debreu, G. 1967. Integration of correspondences. Proceedings of the Fifth Berkeley Symposium on Mathematics, Statistics, and Probability, II, Part 1, eds. L. LeCam, J. Neyman, and E.L. Scott. University of California Press. 351–372.

    Google Scholar 

  28. Dieudonne, J. 1960. Foundations of Modern Analysis. Academic Press.

    Google Scholar 

  29. Dudley, R. M. 1989. Real Analysis and Probability, Wadsworth.

    Google Scholar 

  30. Dugundji, J and V. Granas. 1982. Fixed Point Theory, Polish Scientific Press.

    Google Scholar 

  31. Erikson, J., O. F. Morand and K. L. Reffett. 2004. Isotone Recursive Methods for Overlapping Generations Models. MS. Arizona State University.

    Google Scholar 

  32. Frink, O. 1942. Topology in lattices. Transactions of the American Mathematical Society, 51, 569–582.

    CrossRef  MATH  MathSciNet  Google Scholar 

  33. Gauvin, J. and F. Dubeau. 1982. Differential properties of the marginal function in mathematical programming. Mathematical Programming Studies, 19, 101–119.

    MathSciNet  Google Scholar 

  34. Greenwood, J. and G. Huffman. 1995. On the existence of nonoptimal equilibria in dynamic stochastic economies, Journal of Economic Theory, 65, 611–623.

    CrossRef  Google Scholar 

  35. Guo, D. and V. Lakshmikantham. 1988. Nonlinear Problems in Abstract Cones. Academic Press.

    Google Scholar 

  36. Halmos, P. 1950. Measure Theory, Van Nostrand Press.

    Google Scholar 

  37. Heikkilä, S. 2005. Fixed point results and their applications to Markov processes. MS. Department of Mathematical Sciences, University of Oulu, Finland.

    Google Scholar 

  38. Heikkilä, S. and S. Hu. 1993. On fixed points of multifunctions in ordered spaces. Applicable Analysis, 51, 115–127.

    MathSciNet  Google Scholar 

  39. Heikkilä, S. and V. Lakshmikantham. 1994. Monotone iterative techniques for discontinuous nonlinear differential equations, Marcel Dekker.

    Google Scholar 

  40. Heikkilä, S. and K. Reffett. 2005. Fixed point theorems and their applications to the theory of Nash equilibria, Nonlinear Analysis, forthcoming.

    Google Scholar 

  41. Heikkilä, S. and H. Salonen. 1996. On the existence of extremal stationary distributions of Markov processes. Research report 66, Dept of Economics, Univ. of Turku, Finland.

    Google Scholar 

  42. Heikkilä, S. and H. Salonen. 1996. On approximations of stochastic processes in metric spaces. MS. Dept of Economics, Univ of Turku, Finland.

    Google Scholar 

  43. Hopenhayn, H. and E. Prescott. 1992. Stochastic monotonicity and stationary distributions for dynamic economies. Econometrica, 60, 1387–1406.

    MathSciNet  Google Scholar 

  44. Jachymski, J. 2001. Order-theoretic aspects of metric fixed point theory. in Handbook of Metric Fixed Point Theory, ed. W.A. Kirk and B. Sims, Kluwer. 613–641.

    Google Scholar 

  45. Jachymski, J. 2003. Converses to fixed point theorems of Zermelo and Caristi. Nonlinear Analysis, 52, 1455–63.

    CrossRef  MATH  MathSciNet  Google Scholar 

  46. Judd, K. 1992. Projection methods for solving aggregate growth models. Journal of Economic Theory, 58, 410–452.

    CrossRef  MATH  MathSciNet  Google Scholar 

  47. Kantorovich, L. The method of successive approximation for functional equations. 1939. Acta Math. 71, 63–97.

    Google Scholar 

  48. Krasnosel’skii, M. A., G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitiskii and V. Ya. Stetsenko, 1972. Approximate solution of Operator Equations. Wolters-Noordhoff Press.

    Google Scholar 

  49. Krasnosel’skii, M.A. and P. Zabreiko. 1984. Geometrical Methods of Nonlinear Analysis. Springer-Verlag.

    Google Scholar 

  50. Krebs, T. 2004. Non-existence of recursive equilibria on compact state spaces when markets are incomplete. Journal of Economic Theory, 115, 134–150.

    CrossRef  MATH  MathSciNet  Google Scholar 

  51. Krusell, P. and A. Smith. 1998. Income and wealth heterogeneity in the macroeconomy, Journal of Political Economy, 106, 867–896.

    CrossRef  Google Scholar 

  52. Le Van, C. and Y. Vailakis. 2004. Existence of equilibrium in a single sector model with elastic labor. CERMSEM, Universite Paris I Working Paper.

    Google Scholar 

  53. Li Calzi, M. and A. Veinott, Jr. 1991. Subextremal functions and lattice programming. MS. Stanford University.

    Google Scholar 

  54. Lovejoy, W. 1987. Ordered solutions for dynamic programs. Mathematics of Operations Research, 269–278.

    Google Scholar 

  55. Lucas, R. E., Jr. and N. Stokey. 1987. Money and interest in a cash-inadvance economy. Econometrica, 55, 1821–37.

    MathSciNet  Google Scholar 

  56. Markowsky, G. 1976. Chain-complete posets and directed sets with applications. Algebra Univ, 6, 53–68.

    MATH  MathSciNet  Google Scholar 

  57. Miao, J. 2003. Competitive equilibria in economies with a continuum of consumer and aggregate shocks. Journal of Economic Theory, forthcoming.

    Google Scholar 

  58. Milgrom, P. and C. Shannon. 1994. Monotone comparative statics. Econometrica, 62, 157–180.

    MathSciNet  Google Scholar 

  59. Mirman, L. J., O. F. Morand and K. L. Reffett. 2004. A qualitative approach to Markovian equilibrium in infinite horizon economies with capital. MS. Arizona State University.

    Google Scholar 

  60. Mirman, L. J., K. L. Reffett and J. Stachurski. 2004. Computing Markovian equilibrium in large economies II: Bewley models with aggregate risk. MS. Arizona State University.

    Google Scholar 

  61. Mirman, L. and I. Zilcha. 1975. On optimal growth under uncertainty. Journal of Economic Theory, 11, 329–339.

    CrossRef  MathSciNet  Google Scholar 

  62. Morand, O. and K. Reffett. 2003. Existence and uniqueness of equilibrium in nonoptimal unbounded infinite horizon economies. Journal of Monetary Economics. 50, 1351–1373.

    CrossRef  Google Scholar 

  63. Morand, O. and K. Reffett. 2004. Monotone Map Methods for Overlapping Generations Models with nonclassical technologies: The Case of Markov Shocks. MS. Arizona State University.

    Google Scholar 

  64. Muenzenberger, T. and R. Smithson. 1973. Fixed point structures. American Mathematical Society, 184, 153–173.

    CrossRef  MathSciNet  Google Scholar 

  65. Pelczar, A. 1961 On the invariant points of a transformation. Ann. Pol Math, 11, 199–202.

    MATH  MathSciNet  Google Scholar 

  66. Prescott, E. and R. Mehra. 1980. Recursive competitive equilibrium: the case of homogeneous households. Econometrica, 48, 1365–1379

    Google Scholar 

  67. Reffett, K. L. 2004. Ordered Markovian equilibrium. MS, Arizona State University.

    Google Scholar 

  68. Reffett, K. L. 2004. Mixed monotone fixed point methods with economic applications. MS. Arizona State University.

    Google Scholar 

  69. Reffett, K. L. 2004. Mixed monotone recursivemethods. MS. Arizona State University.

    Google Scholar 

  70. Rockafellar, R. T. 1980. Generalized directional derivatives and subgradients of nonconvex functions. Canadian Journal of Mathematics, 32, 257–280.

    MATH  MathSciNet  Google Scholar 

  71. Rockafellar, R. T. and R. Wets. Variational Analysis. Springer Verlag.

    Google Scholar 

  72. Santos, M. 2000. The numerical accuracy of numerical solutions using Euler residuals. Econometrica, 68, 1377–1400.

    CrossRef  MATH  MathSciNet  Google Scholar 

  73. Santos, M. 2002. On non existence of Markov equilibria in competitivemarket economies. Journal of Economic Theory, 105, 73–98.

    CrossRef  MATH  MathSciNet  Google Scholar 

  74. Santos, M. and J. Vigo-Aguiar. 1998. Analysis of a numerical dynamic programming algorithm applied to economic models. Econometrica, 66, 409–426.

    MathSciNet  Google Scholar 

  75. Smithson, R. 1971. Fixed points of order preserving multifunctions. Proceedings of the American Mathematical Society, 28(1), 304–310.

    CrossRef  MATH  MathSciNet  Google Scholar 

  76. Stokey, N., R. E. Lucas, Jr., with E. Prescott. 1989. Recursive methods in economic dynamics. Harvard Press

    Google Scholar 

  77. Tarski, A. 1949. A fixed point for lattices and its applications. Bull. of Amer. Math. Soc. 55, 1051–52.

    Google Scholar 

  78. Tarski, A. 1955. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics, 5, 285–309.

    MATH  MathSciNet  Google Scholar 

  79. Topkis, D. 1978. Minimizing a submodular function on a lattice. Operations Research, 26, 305–321.

    CrossRef  MATH  MathSciNet  Google Scholar 

  80. Topkis, D. 1979. Equilibrium points in nonzero sum n-person submodular games. SIAM Journal of Control and Optimization, 17, 773–787.

    CrossRef  MATH  MathSciNet  Google Scholar 

  81. Topkis, D. 1998. Supermodularity and Complementarity. Princeton University Press.

    Google Scholar 

  82. Veinott, A. 1989. Lattice Programming, Notes Johns Hopkins University. MS.

    Google Scholar 

  83. Veinott, A. 1992. Lattice programming: qualitative optimization and equilibria. MS. Stanford

    Google Scholar 

  84. Vulikh, B. 1967. Introduction to the Theory of Partially Ordered Spaces, Noordhoff Scientific Publishers.

    Google Scholar 

  85. Zhou, L. 1994. The set of Nash equilibria of a supermodular game is a complete lattice. Games and Economic Behavior, 7, 295–300.

    CrossRef  MATH  MathSciNet  Google Scholar 

  86. Zeidler, E. 1986. Nonlinear Functional Analysis and its Applications, volume 1. Springer Verlag.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Berlin · Heidelberg

About this chapter

Cite this chapter

Datta, M., Reffett, K.L. (2006). Isotone Recursive Methods: The Case of Homogeneous Agents. In: Dana, RA., Le Van, C., Mitra, T., Nishimura, K. (eds) Handbook on Optimal Growth 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32310-4_8

Download citation

Publish with us

Policies and ethics