Optimal Decision Making and the Value of Information in a Time-Dependent Version of the Cost-Loss Ratio Situation

Abstract

A time-dependent version of the cost-loss ratio situation is described and the optimal use and economic value of meteorological information are investigated in this decision-making problem. The time-dependent situation is motivated by a decision maker who contemplates postponing the protect/do not protect decision in anticipation of obtaining more accurate forecasts at some later time (i.e., shorter lead time), but who also recognizes that the cost of protection will increase as lead time decreases. Imperfect categorical forecasts, calibrated according to past performance, constitute the information of primary interest. Optimal decisions are based on minimizing expected expense and the value of information is measured relative to the expected expense associated with climatological information. Accuracy and cost of protection are modeled as exponentially decreasing functions of lead time, and time-dependent expressions for expected expense and value of information are derived. An optimal lead time is identified that corresponds to the time at which the expected expense associated with imperfect forecasts attains its minimum value. The effects of the values of the parameters in the accuracy and cost-of-protection models on expected expense, optimal lead time, and forecast value are examined. Moreover, the optimal lead time is shown to differ in some cases from the lead time at which the economic value of imperfect forecasts is maximized. Numerical examples are presented to illustrate the various results. The implications of these results are discussed and some possible extensions of this work are suggested.