Quantitative Finance

Appendix 1: Probability Theory Basics

A1.1 Introduction

When facing uncertainty, decision making could be hard. Sometimes, simply examining the outcomes is already very useful in making a decision. We have a special mathematical word for outcomes; we call them “events.”

We suppose the events (possible individual outcomes) A, B, C, and so on are subsets of sample space S (possible all outcomes).

Event A or B happens—in set theory language, $A\cup B$ (reads A union B).

Event A and Event B both happen—in set theory language, $A\cap B$ (reads A intersection B).

Event A does not happen—in set theory language. Ac (reads A complement).

(Exclusive or—either A or B happen but not both—$A\cup B-A\cap B).$

Venn diagrams are a good way to visualize these.

The concepts of