ABSTRACT
In this chapter, the authors develop the probability theory needed to model the dynamic behavior of asset prices. The material will require some familiarity with elementary set theory and basic combinatorics. In probability theory, one starts with a given assignment of probabilities to certain subsets of Ω called events. This assignment must satisfy certain axioms and can be quite technical, depending on the sample space and the nature of the events. For a discrete probability space it is possible to assign a probability to each set of outcomes, that is, to each subset of the sample space Ω. In more general circumstances, this sort of flexibility may not be possible, and the assignment of probabilities must be narrowed to a suitably restricted collection of subsets of Ω called an event σ-field.
