Smooth dynamics and computation in models of economic growth

In this paper we give an overview of the differentiability properties of the value and policy functions of dynamic programming. Based upon the differentiability analysis, we also establish approximation estimates for the value and policy functions of a discretized model amenable to the computation of optimal solutions.

[1]  Manuel S. Santos.  On high-order differentiability of the policy function , 1993 .

[2]  E. Denardo.  CONTRACTION MAPPINGS IN THE THEORY UNDERLYING DYNAMIC PROGRAMMING , 1967 .

[3]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[4]  David Easley,et al.  Characterization of optimal plans for stochastic dynamic programs , 1982 .

[5]  R. A. Becker,et al.  Comparative Dynamics in Aggregate Models of Optimal Capital Accumulation , 1985 .

[6]  T. Kehoe.  Computation and multiplicity of equilibria , 1991 .

[7]  Luigi Montrucchio,et al.  Lipschitz continuous policy functions for strongly concave optimization problems , 1987 .

[8]  R. Bellman.  Dynamic programming. , 1957, Science.

[9]  Gerhard Sorger.  Period Three Implies Heavy Discounting , 1994, Math. Oper. Res..

[10]  Itzhak Zilcha,et al.  On optimal growth under uncertainty , 1975 .

[11]  Jose A. Scheinkman,et al.  Duality theory for dynamic optimization models of economics: The continuous time case☆ , 1982 .

[12]  L. Montrucchio,et al.  On the indeterminacy of capital accumulation paths , 1986 .

[13]  M. Falcone.  A numerical approach to the infinite horizon problem of deterministic control theory , 1987 .

[14]  Aloisio Araujo.  The once but not twice differentiability of the policy function , 1991 .

[15]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[16]  Smoothness of the policy function in continuous-time economic models: The one-dimensional case , 1991 .

[17]  R. Lucas.  ASSET PRICES IN AN EXCHANGE ECONOMY , 1978 .

[18]  Manuel S. Santos.  Smoothness of the Policy Function in Discrete Time Economic Models , 1991 .

[19]  Harald Uhlig,et al.  Solving Nonlinear Stochastic Growth Models: a Comparison of Alternative Solution Methods , 1989 .

[20]  Shlomo Sternberg,et al.  On the Structure of Local Homeomorphisms of Euclidean n-Space, II , 1958 .

[21]  D. Levine,et al.  Determinacy of equilibria in dynamic models with finitely many consumers , 1990 .

[22]  Jose A. Scheinkman,et al.  Smoothness, Comparative Dynamics, and the Turnpike Property , 1977 .

[23]  J. Scheinkman,et al.  On the Differentiability of the Value Function in Dynamic Models of Economics , 1979 .

[24]  Differentiability and comparative analysis in discrete-time infinite-horizon optimization , 1992 .

[25]  On the minimum rate of impatience for complicated optimal growth paths , 1992 .

[26]  Nancy L. Stokey,et al.  Recursive methods in economic dynamics , 1989 .

[27]  K. Arrow,et al.  General Competitive Analysis , 1971 .

[28]  J. Danskin.  The Theory of Max-Min and its Application to Weapons Allocation Problems , 1967 .

[29]  F. Clarke.  Generalized gradients and applications , 1975 .