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1 results

  • SPLINE APPROXIMATIONS TO VALUE FUNCTIONS: Linear Programming Approach

  • MICHAEL A. TRICK, STANLEY E. ZIN
  • Journal:
    Macroeconomic Dynamics / Volume 1 / Issue 1 / January 1997
    Published online by Cambridge University Press:
    02 March 2005, pp. 255-277

  • We review the properties of algorithms that characterizethe solution of the Bellman equation of a stochastic dynamic program,as the solution to a linear program. The variables in this problemare the ordinates of the value function; hence, the number ofvariables grows with the state space. For situations in which thissize becomes computationally burdensome, we suggest the use oflow-dimensional cubic-spline approximations to the value function. Weshow that fitting this approximation through linear programmingprovides upper and lower bounds on the solution to the original largeproblem. The information contained in these bounds leads toinexpensive improvements in the accuracy of approximate solutions.