In Chapters 3 and 5, we introduced the horse race investor as an idealization of a decision maker in an uncertain environment. We have analyzed the usefulness of a probabilistic model to this investor, assuming that the investor aims at maximizing his expected wealth growth rate or expected utility. In this chapter we reconsider such an investor who is trying to measure the performance of a probabilistic model. This will lead us to utility-based performance measures for probabilistic models. The main ideas underlying these performance measures can be summarized in the following principle, which is depicted in Figure 8.1. Principle 8.1

(Model Performance Measurement) Given

(i) an investor with a utility function, and

(ii) a market setting (in this chapter, a horse race or a conditional horse race) in which the investor can allocate,

the investor will allocate according to the model (so as to maximize his expected utility under the model).

We will then measure the performance of the candidate model for this investor via the average utility attained by the investor on an out-of-sample test dataset.