Sequential Decision Problems: A Model to Exploit Existing Forecasters

Abstract

A sequential decision problem is partitioned into two parts: a stochastic model describing the transition probability density function of the state variable, and a separate framework of decision choices and payoffs. If a particular sequential decision problem is a recurring one, then there may often exist human forecasters who generate quantitative forecasts at each decision stage. In those eases where construction of a mathematical model for predictive purposes is difficult, we may consider using the forecasts and forecast revisions provided by the existing forecasting mechanism as the state variable. The paper considers a specific class of problems in which improved forecasts of some unknown quantity are available before each decision stage. A small number of actual forecasters are studied through analysis of historical data to see whether the data-generating process for forecast changes is quasi-Markovian. The data are generally, although not entirely, consistent with the hypothesis that ratios of successive forecasts are independent variates; their distribution appears to be conditionally Lognormal. Some possible reasons for these results are explored. In cases where the hypothesis holds, a dynamic programming approach to the sequential decision problem may be used to provide optimal decision rules. The usefulness of the approach is illustrated with a numerical example involving crop planning, and the example is extended to explore the effects of using the methodology when the required assumptions do not hold.

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