The nature of general insurance (MW 1.1) #

General insurance #

• also called non-life, or property and casualty
  • Includes: car, liability, property, workers compensation, marine, credit, legal, travel, health, …
• for more background:
  • see general insurance practice for further details about the general insurance area
  • see Pooling and Insurance for further details about the law of large numbers mechanism

Risk components #

Risk / randomness comes from different sources:

• Pure randomness (also called “process risk” or “aleatoric risk”)
  • Nature of the risk
  • Can be “controlled” by volume (law of large numbers) $$\underset{n\to \mathrm{\infty }}{lim}Pr[|\frac{1}{n}\sum _{i=1}^n{Y}_i-E[Y_i]|\ge ϵ]=0$$
• Model risk (“epistemic risk”)
  All models are wrong, some are useful
  • model world $\ne$ real world
  • even if model was right, wrong parameters
  • non-stationarity

$⟹$ we need to add a buffer to the cost of the risk transfer.

Insurance organises a risk transfer:

• costing of this transfer is an actuarial problem
• makes sense only because people are risk averse, unless insurance is forced: this is because the cost of insurance (the “gross premium”) is always higher than the expected value

Premium components #

$$\begin{array}{rcl}\text{gross premium}& =& \text{pure risk premium}\\ & & +\text{risk margin}\\ & & +\text{profit margin}\\ & & -\text{financial gains on investments}\\ & & +\text{underwriting expenses}\\ & & +\text{loss adjustment expenses (LAE)}\\ & & (+\text{taxes})\end{array}$$

This is not necessarily the premium that is charged to customers, but calculating the right hand side is one of the actuary’s jobs.

Connections with the course contents #

Modules #

• We typically insure multiple risks:
  • We need to know how to aggregate them (Module 2)
  • We need distributions for counts and sums, including random sums (Modules 2, 3, and 4)
  • Those risks may not be independent (Module 5)
• We need a distribution for the losses
  • The “pure risk premium” is the expectation of the risk (Module 3)
  • The “risk margin” is typically function of the distribution of the insured loss–a quantile, or a function of variance (Modules 3 and 4)
  • Sometimes those risks can be extreme (Module 6)
• Losses arise over time, and there may be time dependencies (relationships across time) that are relevant to the modelling
  (Modules 7-10)

R packages used in this course #

The following packages are useful and should be installed and loaded on your machines:

• stats is a generalist package providing statistical functions
• MASS (“Modern Applied Statistics with S”) is a powerful package for data analysis
• tidyverse is a package for wrangling and preparing data for analysis
• actuar is a package with functions that are specific to actuarial studies; see Dutang, Goulet, and Pigeon (2008)
• fitdistrplus builds on the abovementioned packages for advanced fitting features; see Delignette-Muller and Dutang (2015)
• VineCopula and copula packages will be used extensively in Module 5 (Copulas), as well as ggExtra, ggpubr, kdecopula
• evir and extRemes will be used extensively in Module 6 (Extreme Value Theory); see Gilleland and Katz (2016)
• xts, astsa, forecast and vars will be used extensively in Module 7–10
  (Time Series and Analysis)

These packages are the ones (no more, no less) that will be available on your machines for the final exam.

In the lectures that follow, I will indicate which package a function comes from the first time it appears by writing package::function, and then will drop the package:: part as it is not needed once you load that library. [Note this allows you to call a specific function from a package without loading it (useful when there are package clashes).]

References #