Skip to main content
SpringerLink
Log in
Book cover

Handbook on Optimal Growth 1 pp 297–335Cite as

Theory of Stochastic Optimal Economic Growth

  • 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.

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. Amir, R., 1997, A new look at optimal growth under uncertainty, Journal of Economic Dynamics and Control 22(1), 67–86.

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. Athreya, K.B., 2003, Stationary measures for some Markov chain models in ecology and economics, Economic Theory 23(1), 107–22.

    CrossRef  MathSciNet  Google Scholar 

  3. Benhabib, J. and K. Nishimura, 1989, Stochastic equilibrium oscillations, International Economic Review 30(1), 85–102.

    MathSciNet  Google Scholar 

  4. Benveniste, L.M. and J.A. Scheinkman, 1979, On the differentiability of the value function in dynamic models of economics, Econometrica 47(3), 727–32.

    MathSciNet  Google Scholar 

  5. Bertocchi, G. and M. Spagat, 1998, Growth under uncertainty with experimentation, Journal of Economic Dynamics and Control 23(2), 209–31.

    CrossRef  Google Scholar 

  6. Bhattacharya, R.N., and M. Majumdar, 1981, Stochastic models in mathematical economics in Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on “Statistics: Applications and New Directions,” Indian Statistical Institute, Calcutta.

    Google Scholar 

  7. Bhattacharya, R.N. and M. Majumdar, 1999, On a theorem of Dubins and Freedman, Journal of Theoretical Probability 12(4), 1067–87.

    CrossRef  MathSciNet  Google Scholar 

  8. Bhattacharya, R.N. and M. Majumdar, 2001, On a class of random dynamical systems, Journal of Economic Theory 96(1/2), 208–29.

    CrossRef  MathSciNet  Google Scholar 

  9. Bhattacharya, R.N. and M. Majumdar, 2003, Random dynamical systems: a review, Economic Theory 23(1), 13–38.

    CrossRef  MathSciNet  Google Scholar 

  10. Blackwell, D., 1953, Equivalent comparison of experiments, Annals of Mathematical Statistics 24, 265–72.

    MATH  MathSciNet  Google Scholar 

  11. Blackwell, D., 1965, Discounted dynamic programming, Annals of Mathematical Statistics 36, 226–35.

    MATH  MathSciNet  Google Scholar 

  12. Blume, L., Easley, D., and M. O’Hara, 1982, Characterization of optimal plans for stochastic dynamic programs, Journal of Economic Theory 28(2), 221–34.

    CrossRef  MathSciNet  Google Scholar 

  13. Boylan, E.S.,1976, On properties of steady state measures for one-sector growth models, International Economic Review 17(3), 783–85.

    Google Scholar 

  14. Brock, W.A., 1979, An integration of stochastic growth theory and the theory of finance, Part I: The growth model, in General Equilibrium, Growth and Trade, (eds., J.R. Green and J.A. Scheinkman), Academic Press, New York.

    Google Scholar 

  15. Brock, W.A., 1982, Asset prices in an uncertain economy, in The Economics of Information and Uncertainty (ed., J.J. McCall), University of Chicago Press, Chicago.

    Google Scholar 

  16. Brock, W.A. and M.J.P. Magill, 1979, Dynamics under uncertainty, Econometrica 47(4), 843–68.

    MathSciNet  Google Scholar 

  17. Brock, W.A. and M. Majumdar, 1978, Global asymptotic stability results for multisector models of optimal growth under uncertainty where future utilities are discounted, Journal of Economic Theory 18(2), 225–43.

    CrossRef  MathSciNet  Google Scholar 

  18. Brock, W.A. and L.J. Mirman, 1972, Optimal economic growth and uncertainty: the discounted case, Journal of Economic Theory 4(3), 479–513.

    CrossRef  MathSciNet  Google Scholar 

  19. Brock, W.A. and L.J. Mirman, 1973, Optimal economic growth and uncertainty: The no discounting case, International Economic Review 14(3), 560–73.

    MathSciNet  Google Scholar 

  20. Campbell, J. Y., 1994, Inspecting the mechanism: an analytical approach to the stochastic growth model, Journal of Monetary Economics 33(3), 463–506.

    CrossRef  Google Scholar 

  21. Cass, D., 1965, Optimal growth in an aggregative model of capital accumulation, Review of Economic Studies 32, 233–40.

    CrossRef  Google Scholar 

  22. Cass, D. and K. Shell, 1976, The structure and stability of competitive dynamical systems, Journal of Economic Theory 12(1), 31–70.

    CrossRef  MathSciNet  Google Scholar 

  23. Chamberlain, G. and C.A. Wilson, 2000, Optimal intertemporal consumption under uncertainty, Review of Economic Dynamics 3(3), 365–95.

    CrossRef  Google Scholar 

  24. Chang, F.-R., 1982, A note on the stochastic value loss assumption: global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted, Journal of Economic Theory 26(1), 164–70.

    CrossRef  MATH  MathSciNet  Google Scholar 

  25. Dana, R.A., 1974, Evaluation of development programs in a stationary stochastic economy with bounded primary resources, Proceedings of the Warsaw Symposium on Mathematical Models in Economics.

    Google Scholar 

  26. Danthine, J.-P., and J.B. Donaldson, 1981a, Stochastic properties of fast vs. slow growing economies, Econometrica 49(4), 1007–33.

    MathSciNet  Google Scholar 

  27. Danthine, J.-P., and J.B. Donaldson, 1981b, Certainty planning in an uncertain world: a reconsideration, Review of Economic Studies 48(3), 507–10.

    CrossRef  Google Scholar 

  28. Datta, M., 1999, Optimal accumulation in a small open economy with technological uncertainty, Economic Theory 13(1), 207–19.

    CrossRef  MATH  Google Scholar 

  29. Datta, M., L.J. Mirman and E.E. Schlee, 2002, Optimal experimentation in signal dependent decision problems, International Economic Review 43(2), 577–608.

    CrossRef  MathSciNet  Google Scholar 

  30. de Hek, P., 1999, On endogenous growth under uncertainty, International Economic Review 40(3), 727–44.

    CrossRef  ADS  Google Scholar 

  31. de Hek, P. and S. Roy, 2001, On sustained growth under uncertainty, International Economic Review, 42(3), 801–14.

    CrossRef  MathSciNet  Google Scholar 

  32. Dechert, W.D. and K. Nishimura, 1983, A complete characterization of optimal growth paths in an aggregated model with a nonconcave production function, Journal of Economic Theory 31(2), 332–54.

    CrossRef  MathSciNet  Google Scholar 

  33. Diaconis, P., and D. Freedman, 1999, Iterated random functions, SIAM Review 41(1), 45–76.

    CrossRef  MathSciNet  Google Scholar 

  34. Donaldson, J.B., and R. Mehra, 1983, Stochastic growth with correlated production shocks, Journal of Economic Theory 29(2), 282–312.

    CrossRef  MathSciNet  Google Scholar 

  35. Dubins, L.E., and D. Freedman, 1966, Invariant probabilities of certain Markov processes, Annals of Mathematical Statistics 37, 837–47.

    MathSciNet  Google Scholar 

  36. Dutta, P.K., 1987, Capital deepening and impatience-equivalence in stochastic aggregative growth models, Journal of Economic Dynamics and Control 11(4), 519–30.

    CrossRef  MATH  MathSciNet  Google Scholar 

  37. Dutta, P.K., 1991, What do discounted optima converge to? A theory of discount rate asymptotics in economic models, Journal of Economic Theory 55(1), 64–94.

    CrossRef  MATH  MathSciNet  Google Scholar 

  38. Dutta, P.K., Majumdar, M. and R. Sundaram, 1994, Parametric continuity in dynamic programming problems, Journal of Economic Dynamics and Control 18(6), 1069–92.

    CrossRef  MathSciNet  Google Scholar 

  39. Föllmer, H., and M. Majumdar, 1978, On the asymptotic behavior of stochastic economic processes: Two examples from intertemporal allocation under uncertainty, Journal of Mathematical Economics 5(3), 275–88.

    CrossRef  MathSciNet  Google Scholar 

  40. Freixas, X., 1981, Optimal growth with experimentation, Journal of Economic Theory 24(2), 296–309.

    CrossRef  MATH  Google Scholar 

  41. Futia, C., 1982, Invariant distributions and the limiting behavior of Markovian economic models, Econometrica 50(2), 377–408.

    MATH  MathSciNet  Google Scholar 

  42. Hopenhayn, H., and E.C. Prescott, 1992, Stochastic monotonicity and stationary distributions for dynamic economies, Econometrica 60(6), 1387–1406.

    MathSciNet  Google Scholar 

  43. Huggett, M., 2003, When are comparative dynamics monotone? Review of Economic Dynamics 6(1), 1–11.

    CrossRef  Google Scholar 

  44. Inada, K-I, 1963, On a two-sector model of economic growth: comments and a generalization, Review of Economic Studies 30(2), 119–27.

    CrossRef  Google Scholar 

  45. Jaquette, D.L., 1972, A discrete time population control model, Math. Biosciences 15, 231–252.

    CrossRef  MATH  MathSciNet  Google Scholar 

  46. Jeanjean, P., 1974, Optimal development programs under uncertainty: the undiscounted case, Journal of Economic Theory 7(1), 66–92.

    CrossRef  MathSciNet  Google Scholar 

  47. Jones, L.E., and R.E. Manuelli, 1997, The sources of growth, Journal of Economic Dynamics and Control 27(1), 75–114.

    CrossRef  CAS  Google Scholar 

  48. Jones, L.E., Manuelli, R., Siu, H.E. and E. Stacchetti, 2003, Fluctuations in convex models of endogenous growth I: growth effects, Mimeo.

    Google Scholar 

  49. Joshi, S., 1995, Recursive utility and optimal growth under uncertainty, Journal of Mathematical Economics 24(6), 601–17.

    CrossRef  MATH  MathSciNet  Google Scholar 

  50. Joshi, S., 1997, Turnpike theorems in nonconvex nonstationary environments, International Economic Review 38(1), 225–48.

    MATH  MathSciNet  ADS  Google Scholar 

  51. Joshi, S., 2003, The stochastic turnpike property without uniformity in convex aggregate growth models, Journal of Economic Dynamics and Control 27(7), 1289–1315.

    CrossRef  MathSciNet  Google Scholar 

  52. Judd, K.L., 1998, Numerical Methods in Economics, MIT Press, Cambridge, MA.

    Google Scholar 

  53. Kamihigashi, T., 2003, Almost sure convergence to zero in stochastic growth models, Discussion Paper No. 140, RIEB, Kobe University; forthcoming, Economic Theory.

    Google Scholar 

  54. Kamihigashi, T., 2004, Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility, forthcoming, Journal of Economic Dynamics and Control.

    Google Scholar 

  55. Koopmans, T.C., 1957, Three Essays on the State of Economic Science, McGraw-Hill, New York.

    Google Scholar 

  56. Koopmans, T., 1965, On the concept of optimal economic growth, in Semaine d’Etude sur le Rôle de l’Analysis Econometrique dans la Formulation de plans de Development, Pontifican Academiae Scientiarium Scripta Varia No. 28, Vatican.

    Google Scholar 

  57. King, R.G., Plosser, C.I., and S.T. Rebelo, 1988, Production, growth and business cycles I: The basic neoclassical model, Journal of Monetary Economics 21(2/3), 195–232.

    CrossRef  Google Scholar 

  58. King, R.G., C.I. Plosser and S.T. Rebelo, 2002, Production, growth and business cycles: technical appendix, Computational Economics 20(1–2), 87–116.

    CrossRef  Google Scholar 

  59. Kurz, M., 1968, Optimal economic growth and wealth effects, International Economic Review 9, 348–357.

    MATH  Google Scholar 

  60. Kydland, F. and E.C. Prescott, 1982, Time to build and aggregate fluctuations, Econometrica 50(6), 1345–70.

    Google Scholar 

  61. Le Van, C. and J. Stachurski, 2004, Parametric continuity of stationary distributions, Research Paper No. 899, Dept. of economics, The University of Melbourne, Australia.

    Google Scholar 

  62. Leland, H., 1974, Optimal growth in a stochastic environment, Review of Economic Studies 41(1), 75–86.

    CrossRef  MATH  Google Scholar 

  63. Levhari, D. and T.N. Srinivasan, 1969, Optimal savings under uncertainty, Review of Economic Studies 36,153–63.

    CrossRef  Google Scholar 

  64. Long, J.B. and C.I. Plosser, 1983, Real business cycles, Journal of Political Economy 91(1), 39–69.

    CrossRef  Google Scholar 

  65. Magill, M., 1977, A local analysis of n-sector capital accumulation under uncertainty, Journal of Economic Theory 15(1), 211–18.

    CrossRef  MATH  MathSciNet  Google Scholar 

  66. Maitra, A., 1968, Discounted dynamic programming on compact metric spaces, Sankhya Ser. A 30, 211–16.

    MATH  MathSciNet  Google Scholar 

  67. Majumdar, M., 1982, A note on learning and optimal decisions with a partially observable state space, in Essays in the Economics of Renewable Resources (Eds., L.J. Mirman and D. Spulber), North Holland, Amsterdam.

    Google Scholar 

  68. Majumdar, M. and T. Mitra, 1982, Intertemporal allocation with a nonconvex technology: the aggregative framework, Journal of Economic Theory 27(1), 101–36.

    CrossRef  MathSciNet  Google Scholar 

  69. Majumdar, M., Mitra, T. and Y. Nyarko, 1989, Dynamic optimization under uncertainty: non-convex feasible sets, in Joan Robinson and Modern Economic Theory (ed. G.R. Feiwel), Macmillan Press, New York, 1989, 545–90.

    Google Scholar 

  70. Majumdar, M. and R. Radner, 1983, Stationary optimal policies with discounting in a stochastic activity analysis model, Econometrica 51(6), 1821–37.

    MathSciNet  Google Scholar 

  71. Majumdar, M. and I. Zilcha, 1987, Optimal growth in a stochastic environment: some sensitivity and turnpike results, Journal of Economic Theory 43(1), 116–33.

    CrossRef  MathSciNet  Google Scholar 

  72. Malinvaud, E., 1953, Capital accumulation and efficient allocation of resources, Econometrica 21, 233–68.

    MATH  MathSciNet  Google Scholar 

  73. Marimon, R., 1989, Stochastic turnpike property and stationary equilibrium, Journal of Economic Theory 47(2), 282–306.

    CrossRef  MATH  MathSciNet  Google Scholar 

  74. Marimon, R. and A. Scott, 1999, Computational Methods for the Study of Dynamic Economies, Oxford, Oxford University Press.

    Google Scholar 

  75. McKenzie, L.W., 1976, Turnpike theory, Econometrica 44(5), 841–65.

    MATH  MathSciNet  Google Scholar 

  76. McKenzie, L.W., 1986, Optimal economic growth, turnpike theorems and comparative dynamics, in Handbook of Mathematical Economics: Volume III (Eds., K.J. Arrow and M.D. Intriligator), North Holland, Amsterdam.

    Google Scholar 

  77. McKenzie, L.W., 1998, Turnpikes, American Economic Review 88(2), 1–14.

    Google Scholar 

  78. Mendelssohn, R., and M. Sobel, 1980, Capital accumulation and the optimization of renewable resource models, Journal of Economic Theory 23(2), 243–60.

    CrossRef  Google Scholar 

  79. Merton, R.C., 1975, An asymptotic theory of growth under uncertainty, Review of Economic Studies 42(3), 375–93.

    CrossRef  Google Scholar 

  80. Miller, B., 1976, The effect on optimal consumption of increased uncertainty in labor income in the multiperiod case, Journal of Economic Theory 13(1), 154–67.

    CrossRef  MATH  MathSciNet  Google Scholar 

  81. Mirman, L.J., 1972, On the existence of steady-state measures for one sector growth models, International Economic Review 13(2), 271–86.

    MATH  MathSciNet  Google Scholar 

  82. Mirman, L.J., 1980, One sector economic growth and uncertainty: a survey, in Stochastic Programming (ed., M.A.H. Dempster), Academic Press, London, 537–67.

    Google Scholar 

  83. Mirman, L.J. and D.F. Spulber, 1984, Uncertainty and markets for renewable resources, Journal of Economic Dynamics and Control 8(3), 239–64.

    CrossRef  MathSciNet  Google Scholar 

  84. Mirman, L.J. and D.F. Spulber, 1985, Fishery regulation with harvest uncertainty, International Economic Review 26(3), 731–46.

    MathSciNet  Google Scholar 

  85. Mirman, L.J. and I. Zilcha, 1975, On optimal growth under uncertainty, Journal of Economic Theory 11(3), 329–39.

    CrossRef  MathSciNet  Google Scholar 

  86. Mirman, L.J. and I. Zilcha, 1976, Unbounded shadow prices for optimal stochastic growth models with uncertain technology, International Economic Review 17(1), 121–32.

    MathSciNet  Google Scholar 

  87. Mirman, L.J. and I. Zilcha, 1977, Characterizing optimal policies in a one-sector model of economic growth under uncertainty, Journal of Economic Theory 14(2), 389–401.

    CrossRef  MathSciNet  Google Scholar 

  88. Mirrlees, J.A., 1974, Optimal accumulation under uncertainty: the case of stationary returns of investment, in Allocation under Uncertainty: Equilibrium and Optimality” (Ed., J. Drèzé), Wiley, New York.

    Google Scholar 

  89. Mitra, K., 1998, On capital accumulation paths in a neoclassical stochastic growth model, Economic Theory 11, 457–64.

    CrossRef  MATH  MathSciNet  Google Scholar 

  90. Mitra, T., and Y. Nyarko, 1991, On the existence of optimal processes in nonstationary environments, Journal of Economics 53(3), 245–70.

    MathSciNet  Google Scholar 

  91. Mitra, T. and F. Privileggi, 2004, Cantor type invariant distributions in the theory of optimal growth under uncertainty, Journal of Difference Equations and Applications, 10, 489–500.

    CrossRef  MathSciNet  Google Scholar 

  92. Mitra, T., Montrucchio, L., and F. Privileggi, 2003, The nature of steady states in models of optimal growth under uncertainty, Economic Theory 23(1), 39–71.

    CrossRef  MathSciNet  Google Scholar 

  93. Mitra, T. and S. Roy, 2006, Optimal exploitation of renewable resources under uncertainty and the extinction of species, Economic Theory 28(1), 1–23.

    CrossRef  MathSciNet  Google Scholar 

  94. Montrucchio, L., and F. Privileggi, 1999, Fractal steady states in stochastic optimal control models, Annals of Operations Research 88, 183–97

    CrossRef  MathSciNet  Google Scholar 

  95. Nishimura, K., Rudnicki, R., and J. Stachurski, 2003, Stochastic optimal growth with non-convexities, Mimeo., Institute of Economic Research, Kyoto University.

    Google Scholar 

  96. Nishimura, K. and J. Stachurski, 2004, Stability of Stochastic Optimal Growth Models: A New Approach, forthcoming, Journal of Economic Theory.

    Google Scholar 

  97. Nyarko, Y. and L.J. Olson, 1991, Stochastic dynamic models with stock-dependent rewards, Journal of Economic Theory 55(1), 161–68.

    CrossRef  MathSciNet  Google Scholar 

  98. Nyarko, Y. and L.J. Olson, 1994, Stochastic growth when utility depends on both consumption and the stock level, Economic Theory 4(5), 791–97.

    CrossRef  Google Scholar 

  99. Nyarko, Y. and L.J. Olson, 1996, Optimal growth with unobservable resources and learning, Journal of Economic Behavior and Organization 29(3), 465–91.

    CrossRef  Google Scholar 

  100. Olson, L.J., 1989, Stochastic growth with irreversible investment, Journal of Economic Theory 47(1), 101–29.

    CrossRef  MATH  MathSciNet  Google Scholar 

  101. Olson, L.J. and S. Roy, 1996, On conservation of renewable resources with stock-dependent return and nonconcave production, Journal of Economic Theory 70(1), 133–157.

    CrossRef  Google Scholar 

  102. Olson, L.J. and S. Roy, 2000, Dynamic efficiency of conservation of renewable resources under uncertainty, Journal of Economic Theory 95(2), 186–214.

    CrossRef  MathSciNet  Google Scholar 

  103. Phelps, E.S., 1962, The accumulation of risky capital: a sequential utility analysis, Econometrica 30, 729–43.

    MATH  Google Scholar 

  104. Prescott, E.C., and R. Mehra, 1980, Recursive competitive equilibrium: the case of homogenous households, Econometrica 48(6), 1365–79.

    Google Scholar 

  105. Radner, R., 1961, Paths of economic growth that are optimal with regard only to final states, Review of Economic Studies 28, 98–104.

    CrossRef  Google Scholar 

  106. Radner, R., 1973, Optimal stationary consumption with stochastic production and resources, Journal of Economic Theory 6(1), 68–90.

    CrossRef  MathSciNet  Google Scholar 

  107. Reed, W.J., 1974, A stochastic model for the economic management of a renewable resource,Mathematical Biosciences 22(4), 313–37.

    CrossRef  MATH  MathSciNet  Google Scholar 

  108. Ramsey, F.P., 1928, A mathematical theory of savings, Economic Journal 38, 543–59.

    CrossRef  Google Scholar 

  109. Razin, A. and J.A. Yahav, 1979, On stochastic models of economic growth, International Economic Review 20(3), 599–604.

    MathSciNet  Google Scholar 

  110. Rockafellar, R.T., 1976, Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate, Journal of Economic Theory 12(1), 71–113.

    CrossRef  MATH  MathSciNet  Google Scholar 

  111. Rothschild, M., and J.E Stiglitz, 1971, Increasing risk II: its economic consequences, Journal of Economic Theory 3(1), 66–84.

    CrossRef  MathSciNet  Google Scholar 

  112. Rust, J., 1996, Numerical Dynamic Programming in Economics, in Handbook of Computational Economics (Eds, H.M. Amman, D.A. Kendrick and J. Rust) Elsevier, Amsterdam, 619–729.

    Google Scholar 

  113. Santos, M., 1999, Numerical solutions of dynamic economic models, in Handbook of Macroeconomics (Eds., J.B. Taylor and M. Woodford) v. 1A, ch. 5, Elsevier, Amsterdam.

    Google Scholar 

  114. Santos, M.S., 2000, Accuracy of numerical solutions using the Euler equation residuals, Econometrica 68(6), 1377–1402.

    CrossRef  MATH  MathSciNet  Google Scholar 

  115. Santos, M.S., and A. Peralta-Alva, 2003, Accuracy of simulations for stochastic dynamic models, Mimeo.

    Google Scholar 

  116. Santos, M.S., and J.T. Vigo-Aguiar, 1998, Analysis of a numerical dynamic programming algorithm applied to economic models, Econometrica 66(2), 409–26.

    MathSciNet  Google Scholar 

  117. Sargent, T.J.,1980, Tobin’s ‘q’ and the rate of investment in general equilibrium, in On The State of Macroeconomics (eds., K. Brunner and A.H. Meltzer), North-Holland, Amsterdam, 107–54.

    Google Scholar 

  118. Schäl, M., 1975, Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal, Z. Wahrscheinlichkeitstheorie verw. Gebiete 32, 179–96.

    CrossRef  MATH  Google Scholar 

  119. Schechteman, J., 1976, An income fluctuation problem, Journal of Economic Theory 12(2), 218–41.

    CrossRef  MathSciNet  Google Scholar 

  120. Schechteman, J. and V. Escudero, 1977, Some results on an ‘An income fluctuations problem’, Journal of Economic Theory 16, 151–66.

    CrossRef  MathSciNet  Google Scholar 

  121. Serfozo, R., 1976, Monotone optimal policies for Markov decision processes, Math. Prog. Study 6, 202–15.

    MATH  MathSciNet  Google Scholar 

  122. Sotomayor, M., 1984, On income fluctuations and capital gains, Journal of Economic Theory 32(1), 14–35.

    CrossRef  MATH  MathSciNet  Google Scholar 

  123. Spulber, D.F., 1982, Adaptive harvesting of a renewable resource and stable equilibrium, in Essays in the Economics of Renewable Resources (eds., L.J. Mirman and D.F. Spulber) North Holland, Amsterdam.

    Google Scholar 

  124. Stachurski, J., 2002, Stochastic optimal growth with unbounded shock, Journal of Economic Theory 106(1), 40–65.

    CrossRef  MATH  MathSciNet  Google Scholar 

  125. Stachurski, J., 2003, Stochastic growth: asymptotic distributions, Economic Theory 21(4), 913–19

    CrossRef  MATH  MathSciNet  Google Scholar 

  126. Stokey, N.L., Lucas, R.E., and E.C. Prescott, 1989, Recursive Methods in Economic Dynamics, Harvard University Press, Massachusetts.

    Google Scholar 

  127. Strauch, R., 1966, Negative dynamic programming, Annals of Mathematical Statistics 37, 871–90.

    MATH  MathSciNet  Google Scholar 

  128. Sutherland, W.R.S., 1970, On optimal development in a multi-sectoral economy: the discounted case, Review of Economic Studies 37, 585–89.

    CrossRef  MATH  Google Scholar 

  129. Topkis, D., 1978, Minimizing a submodular function on a lattice, Operations Research 26(2), 305–21.

    CrossRef  MATH  MathSciNet  Google Scholar 

  130. Taylor, J.B. and H. Uhlig, 1990, Solving nonlinear stochastic growth models: a comparison of alternative solution methods, J. Bus. Econ. Stat. 8(1), 1–17.

    CrossRef  Google Scholar 

  131. Williams, N., 2004, Small noise asymptotics for a stochastic growth model, Journal of Economic Theory, 119(2), 271–98.

    CrossRef  MATH  MathSciNet  Google Scholar 

  132. Yaari, M.E., 1976, A law of large numbers in the theory of consumer’s choice under uncertainty, Journal of Economic Theory 12, 202–17.

    CrossRef  MATH  MathSciNet  Google Scholar 

  133. Yano, M., 1989, Comparative statics in dynamic stochastic models: differential analysis of a stochastic modified golden rule in a Banach space, Journal of Mathematical Economics 18(2), 169–85.

    CrossRef  MATH  MathSciNet  Google Scholar 

  134. Zilcha, I., 1975, Weakly maximal optimal stationary programs under uncertainty, International Economic Review 16(3), 796–99.

    MATH  MathSciNet  Google Scholar 

  135. Zilcha, I., 1976a, Characterization by prices of optimal programs under uncertainty, Journal of Mathematical Economics 3, 173–84.

    CrossRef  MATH  MathSciNet  Google Scholar 

  136. Zilcha, I, 1976b, On competitive prices in a multisector economy with stochastic production and resources, Review of Economic Studies 43(3), 431–38.

    CrossRef  MATH  Google Scholar 

  137. Zilcha, I., 1978, Transversality conditions in a multisector economy under uncertainty, Econometrica 46(3), 505–26.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Maryland, College Park, MD, USA

    Lars J. Olson

  2. Southern Methodist University, Dallas, TX, USA

    Santanu Roy

Authors
  1. Lars J. Olson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Santanu Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CEREMADE, University of Paris IX Dauhine, Place du Marechal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Rose-Anne Dana

  2. CERMSEM, University of Paris 1 — Pantheon Sorbonne, 106-112 boulevard de l’Hopital, 75013, paris, France

    Cuong Le Van

  3. Department of Economics, Cornell University, Ithaca, NY, 14853, USA

    Tapan Mitra

  4. Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-hu, Kyoto, 606-8501, Japan

    Kazuo Nishimura

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Berlin · Heidelberg

About this chapter

Cite this chapter

Olson, L.J., Roy, S. (2006). Theory of Stochastic Optimal Economic Growth. 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_11

Download citation

Publish with us

Policies and ethics

search

Navigation