Repetitive Decision Making and the Value of Forecasts in the Cost‐Loss Ratio Situation: A Dynamic Model

Abstract

The purposes of this paper are to describe a dynamic model for repetitive decision?making in the cost?loss ratio situation and to present some theoretical and numerical results related to the optimal use and economic value of weather forecasts within the framework of the model. This model involves the same actions and events as the standard (i.e., static) cost?loss ratio situation, but the former (unlike the latter) is dynamic in the sense that it possesses characteristics (e.g., decisions, events) that are related over time. We assume that the decision maker wants to choose the sequence of actions over an n?occasion time period that minimizes the total expected expense. A computational technique known as stochastic dynamic programming is employed to determine this optimal policy and the total expected expense. Three types of weather information are considered in studying the value of forecasts in this context: 1) climatological information; 2) perfect information; and 3) imperfect forecasts. Climatological and perfect information represent lower and upper bounds, respectively, on the quality of all imperfect forecasts, with the latter considered here to be categorical forecasts properly calibrated according to their past performance. Theoretical results are presented regarding the form of the optimal policy and the relationship among the total expected expenses for these three types of information. In addition, quality/value relationships for imperfect forecasts are described. Numerical results are derived from the dynamic model for specific values of the model parameters. These results include the optimal policy and the economic value of perfect and imperfect forecasts for various time horizons, climatological probabilities, and values of the cost?loss ratio. The relationship between the accuracy and value of imperfect forecasts also is examined. Several possible extensions of this dynamic model are briefly discussed, including decision?making problems involving more actions and/or events, more complex structures of the costs and losses, and more general forms of imperfect forecasts (e.g., probability forecasts).