# Quantitative Fundamentals

## 2.1 INTRODUCTION

This chapter outlines the mathematical and statistical concepts that underpin the risk models used throughout this book. Readers already familiar with these concepts can readily skip to Chapter 3. This chapter provides an outline of the range of topics used in this book, rather than providing complete details. Reference suggestions are provided throughout, in order for the interested reader to obtain a deeper mastery.

The most fundamental concept in risk theory is that of a random variable. Random variables are particularly important for risk models, since risk is associated with financial and business outcomes that are typically unpredictable. Risk management is concerned with gauging the level of unpredictability (risk measurement), determining an appropriate tolerance level (risk appetite) and determining strategies for control and management of any residual exposure.

A random variable is itself an unpredictable quantity, which can take any value in a defined sample space Ω. Thus, a sample space represents the range of values (or outcomes) that a random variable can take, eg, {1, 2, 3, 4, 5, 6} for a simple die. Typical sample spaces seen in risk models