# The Econometrics of Individual Risk: Credit, Insurance, and Marketing

Christian Gourieroux
Joann Jasiak
Pages: 256
https://www.jstor.org/stable/j.ctt7t5fb

1. Front Matter
(pp. i-vi)
(pp. vii-x)
3. Preface
(pp. xi-xiv)
4. 1 Introduction
(pp. 1-6)

People and businesses operate in uncertain environments and bear a variety of risks. As the service sector of the economy grows rapidly, the risk exposure of financial institutions, insurers, and marketers becomes more and more substantial. The risks grow and diversify in parallel with the offering of market and retail financial products, insurances, and marketing techniques. Private businesses adapt to the increasingly risky environment by implementing quite sophisticated, and often costly, systems of risk management and control. Recent corporate history has proven, however, that these are far from flawless and that financial losses can be devastating.

The risk can be...

5. 2 Dichotomous Risk
(pp. 7-22)

The probability of the occurrence of a loss event is measured on a scale from zero to one. This chapter presents simple models for assessing the probability of a loss event represented by a dichotomous qualitative random variable.

Formally, let the loss event be denoted byAand consider the following random variable defined as the indicator of eventA:${{\textbf 1}_{A}}=\left\{ \begin{array}{*{35}{l}} 1 & \text{if }A\text{ occurs,} \\ 0 & \text{if }A\text{ does not occur}\text{.} \\ \end{array} \right.$

It is clear thatY= 1 − 1Ais a random variable that takes the value 0 ifAoccurs and 1 otherwise. Both variables 1AandYtake only two values, and are therefore called dichotomous qualitative...

6. 3 Estimation
(pp. 23-42)

There are a variety of statistical data-based methods for computation and analysis of scores. In this chapter, we assume that a set of data on risk and individual covariates is available, and that we also have access to statistical software for numerical implementations. Formally, the data on both risk and individual covariates are required to be i.i.d., that is, to contain observations which are independently and identically distributed. This assumption is satisfied when the sample of observed individuals is random, that is, when each observation is drawn independently with identical probability from the same population. It becomes violated whenever unequal...

7. 4 Score Performance
(pp. 43-60)

A high-quality score is expected to perform well in distinguishing between “bad” and “good” risk individuals. From a statistical point of view, it is unlikely that indications of a score are correct in 100% of cases. There exist methods that assess and enhance the power of a score in order to keep the error margin to a minimum. The power of a score can deteriorate or improve in time, or vary across different populations. In order to avoid flaws in individual risk prediction, scores need to be monitored and adjusted, if necessary. The main diagnostic tool used by the professionals...

8. 5 Count Data Models
(pp. 61-84)

The risk models discussed so far are based on the dichotomous risk variable, which indicates whether or not a loss event occurs. In this chapter, we will investigate how many loss events occur per unit of time or, equivalently, how frequent the loss events are. In technical terms, counting the number of losses per unit of time means shifting our attention to risk viewed as a count variable. In the insurance system, for example, important count variables include the number of claims on one policy in one year, the number of payments on one policy in one year, and the...

9. 6 Durations
(pp. 85-112)

The last type of risk variable discussed in this book is the duration variable, or, equivalently, the time-to-loss. This approach to risk assessment emphasizes the timing of a loss event. The following durations are commonly encountered in insurance and finance: the time-to-death from the date insurance was purchased for a life insurance policy; the time from occurrence of a disabling event to recovery or death for a health insurance policy; the time-to-default on a loan; and the time-to-prepayment on a loan or a mortgage that terminates early.

Like any random variable, a duration variable can be defined by its density...

10. 7 Endogenous Selection and Partial Observability
(pp. 113-128)

The statistical methods introduced in previous chapters concerned samples of individuals drawn randomly from the same population. Under this assumption, all individual observations in a sample are i.i.d., that is, independently and identically distributed. In addition, the endogenous risk variables were assumed to be completely observed. These two assumptions are not always satisfied, for various reasons. In this chapter, we discuss statistical methods applicable to nonhomogeneous samples and partially observed variables. The first part covers estimation of individual risk from stratified samples, under exogenous and endogenous stratification schemes. The model relies on the dichotomous qualitative variable risk representation. We will...

11. 8 Transition Models
(pp. 129-148)

In this chapter we study individual histories recorded in discrete time. For each individuali,i= 1, . . . ,n, the history is formed by a sequence of observationsYi,t,t= 0, 1, . . . ,Ti(say), with values in a finite state space. In general, the states are qualitative. To facilitate analytical computations we assign a dummy variable, whose values indicate one of theJqualitative statesj= 1, . . . ,Jobserved at a given time. For example, each firm among the corporate bonds issuers has an individual history...

12. 9 Multiple Scores
(pp. 149-180)

In basic models for qualitative, count, and duration data presented in Chapters 2–6, the impact of individual covariates on the distribution of risk is summarized by a unique score. The advantage of using a unique score is that it allows for ranking individuals without ambiguity. However, in the presence of multiple risks, it is preferable to consider a set of scores with different interpretations. This approach was already adopted in the section of Chapter 7 on partial observability, and in Chapter 8 on transition models. In this chapter, further insights on multi-score analysis will be provided.

The problems to...

13. 10 Serial Dependence in Longitudinal Data
(pp. 181-208)

This chapter is concerned with an intersection between the topics of time-series and panel-data econometrics. Each of these is a wide and quickly growing field, described in a number of monographs. Therefore, thorough coverage of the related econometric methodology is beyond the scope of this book. Instead, we focus our attention on a few selected models for a specific class of stochastic processes. A stochastic process (also called a time series) is a sequence of realizations of a random variable in time. The realizations can be independent¹ or serially correlated (autocorrelated). An example of a class of stochastic processes is...

14. 11 Management of Credit Risk
(pp. 209-238)

In the last decade, the number and complexity of financial products has increased significantly. In response to this phenomenon, a banking supervisory committee was established in Basel (Basle), Switzerland. The objectives of the Basle Committee are the development and worldwide coordination of risk control and management methods. In 1995, the Basle Committee signed a document called the Basle Accord, in which it imposed mandatory rules for determining the amount of capital reserve as an instrument of market risk control. These rules are based on a risk measure, called theValue-at-Risk(VaR). The VaR is used to determine the minimum capital...

15. Index
(pp. 239-241)