Sensitivity Analysis of Optimal Linear Random Parameter Systems.
Abstract
This report involves the application of ideas in adaptive stochastic control to economics. We investigate the control problem for a linear, multivariable, dynamic system with purely random (i.e. white) parameters. The quadratic cost criterion is formulated to make the problem a tracking problem. Since the parameters are modelled as white stochastic processes, there is no posterior learning and no dual effect. The certainty-equivalence principle does not hold. We find that the extension of the Uncertainty Threshold Principle from scalar systems to multidimensional ones turns out to be analytically intractable. Next, we derive sensitivity equations for the above optimal system to study the effects of small variations in parameter uncertainties on the optimal performance of the system. These equations enable us to rank parameters in order of the sensitivity of the performance to variations in their variances. This makes it possible to locate the 'pressure' points in a model, if any exist. We then convert an economic policy problem into a stochastic optimal control tracking problem and analyse it with the equations we have derived. We study the different elements that enter into a tracking problem and then discuss the empirical results obtained from the sensitivity equations. The model we choose for the analysis turns out to be insensitive to variations in parameter variances which makes it reasonably reliable. We also analyse in detail the structure of the model and the interdependences of the state and control variables.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1979
- Accession Number
- ADA071091
Entities
People
- Prashant Parikh
Organizations
- Massachusetts Institute of Technology