Bayesian Analysis of Stochastic Process Models

10

Risk analysis

10.1 Introduction

This book was written in times of economic recession and high market volatility with various countries having had to undertake drastic action to reduce spending. Lack of faith by investors in the Euro zone has led to large daily variations in the standard stock market indices such as S&P and Dow Jones. Furthermore, we have recently seen a large number of both natural and man-made disasters. The Icelandic volcano Eyjafjallajökull erupted in 2010 causing air transport chaos and a tsunami in Japan in early 2011 caused damage to a nuclear installation and massive costs to the Japanese economy. Clearly, disasters of this type lead to great financial losses for the individuals or companies affected and for their insurers.

Given the scale of the possible losses that can occur from risky investments and the possibility of insurers being ruined by having to make massive payouts, it is important to study problems of risk and ruin from a statistical viewpoint. How can investors or financial institutions such as banks evaluate the risk in the market at a given moment and how can companies or their insurers calculate their probability of being ruined? Clearly, profits from investments or insurance losses over time follow stochastic processes. This motivates their study in this chapter, which is organized as follows.

In Section 10.2, we first consider how to measure market risk and then how to use Bayesian modeling of financial time series to estimate market ...