Robust Control: A Note on the Response of the Control to Changes in the "Free" Parameter Conditional on the Character of Nature

  • Authors:

  • Fidel Gonzalez;Arnulfo Rodriguez

  • Affiliations:

  • Economic and Housing Analysis Unit, Sociedad Hipotecaria Federal (SHF), Mexico City;Economic Studies Division, Bank of Mexico, Mexico City

  • Venue:
  • Computational Economics
  • Year:
  • 2004

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Abstract

In this paper an analytical framework similar to a robust control problem was developed for the one-state, one-control variable model to examine the response of the control to changes in the "free" parameter. However, in contrast to Gonzalez and Rodriguez (2003), the sign multiplying the "free" parameter in the criterion function of the min--max problem is positive. We find that this set up corresponds to the case where nature is benevolent while the problem posed by Gonzalez and Rodriguez (2003) corresponds to a malevolent nature. We show that for the benevolent case, the solution is a minimum giving way to an ordinary control problem. In addition, the left side of the discontinuity in Gonzalez and Rodriguez (2003) corresponds to the benevolent case.