Comparative Dynamics (Sensitivity Analysis) in Optimal Control Theory
HARVARD UNIV CAMBRIDGE MA
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The paper considers an optimal control problem with a parameter and develops a systematic method for comparative dynamics. A sufficient condition for the optimum solution to be differentiable with respect to the parameter is provided. Formulas for computing the derivative are given in the form of initial-value problems of linear differential equations. Possibility of discontinuous optimal controls is fully taken care of. The derivative of the maximized objective function with respect to the parameter is expressed in a simple form by using the auxiliary variables. An example of the comparative dynamics is given in terms of a model of optimal capital accumulation.
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