Impulse controls and uncertainty in economics: Method and application. (March 2015) - Chu, Long; Kompas, Tom; Grafton, Quentin
Abstract: We develop a stochastic optimal control framework to address an important class of economic problems where there are discontinuities and a decision maker is able to undertake impulse controls in response to unexpected disturbances. Our contribution is two fold: (1) to develop a linear programming algorithm that produces a consistent approximation of the maximum value and optimal policy functions in the context of stochastic impulse controls; and (2) to illustrate the economic benefits of impulse controls optimized, using our framework, and calibrated to the population dynamics of a marine fishery. We contend that the framework has wide applicability and offers the possibility of higher economic pay-off for a wide-range of policy problems in the presence of discontinuities and adverse shocks. Highlights: We develop an optimal impulse control in response to unexpected disturbances. We propose a linear programming algorithm to numerically solve the impulse control. The model is illustrated with an example of relocatable marine reserves. The example shows the economic benefit of reserves even if fish mobility is small.