Freakonometrics

I will be giving in less than four weeks a short course at the 6th R/Rmetrics Meielisalp Workshop & Summer School on Computational Finance and Financial Engineering organized by ETH Zürich, https://www.rmetrics.org/. The talk will be on Actuarial models with R, and first part will be dedicated to life insurance. A complete set of slides can be downloaded from the blog, but in the talk, only some part will be presented.

The codes are from a book on actuarial science in R, written with Christophe Dutang and Vincent Goulet (so far in French) that should appear, some day... The code used in the slides can be downloaded from here, and datasets are the following,

> TD <- read.table(
+ "http://perso.univ-rennes1.fr/arthur.charpentier/TD8890.csv",
+ sep=";",header=TRUE)
> TV <- read.table(
+ "http://perso.univ-rennes1.fr/arthur.charpentier/TV8890.csv",
+ sep=";",header=TRUE)

For additional resources, I recommend Emiliano's website, http://www.math.uconn.edu/, with great lectures on life insurance mathematics, and the (new) lifecontinfencies vignette on http://cran.r-project.org/,

> library(lifecontingencies)

I read yesterday an interesting review of the book written by Bjørn Lomborg, which proposes an economic analysis (the subtitle being "comparing costs and benefits") of climate change. Actually, it is a collective book written by the Copenhagen Business School. Martin L. Weitzman (here) wrote a nice review in Nature, a few week ago, precisely untitled 'Insurance for a warming planet'. As Martin Weitzman wrote it, surprisingly, there is no real discussion about uncertain in the book: "key parameters
are approximated by firm values, such as the median or mean, rather than a probability distribution. The modelling thus becomes a knobt-widdling exercise in optimizing outcomes". And to go further, "The economics of climate change is mainly about decision-making under extreme uncertainty [...] A striking feature of the economics of climate change is that rare but catastrophic events may have unfathomable costs. Deep uncertainty about the unknown unknowns of what might go wrong is therefore coupled with essentially unlimited liability. The resulting battle between declining probabilities and increasing damages is difficult to resolve. Alas, this uncertainty can figure prominently in evaluations of climate change policies. Its absence in a book dealing with economic comparisons of smart solutions is a serious omission [...] When confronted with the possibility of extreme damages at low probabilities, most people do not look to averages. Instead they think about how much insurance they need, and can afford to buy, to survive those events. Climate policy is better viewed as buying insurance for the planet against extreme outcomes than as the solution to a multivariate problem over which we have control".

The insurance works in France only because of the cat nat system. We can see on that picture that there are two different regions in France: the one in white, i.e. no drought over the past 20 years, and the one with small dots, i.e. droughts every 5 or 10 years. This heterogeneity might probably end the market, in the case the cat nat system does not work any longer. In several regions, no one will buy such insurance (why getting insurance if there is no risk ?), while in other, everyone will. And then, we might face some bankruptcies since risks become too correlated in those small regions... Anyway, if you're interested in droughts, you can look here, or there, or here if you want (in French) a description of the cat nat system.
This was the starting point of a paper we started a few years ago with Benoît, untitled "Natural Catastrophe Insurance: When Should the Government Intervene? ". The paper is now on-line, and can be downloaded from here.
The abstract is the following "The present research relaxes three of the usual assumptions made in the insurance literature. It is assumed that (1) there is a finite number of risks, (2) the risks are not statistically independent and (3) the structure of the market is monopolistic. In this context, the article analyses two models of natural catastrophe insurance: a model of insurance with limited liability and a model with unlimited guarantee. Among others, the results confirm the idea that the natural catastrophe insurance industry is characterized by economies of scale. The government should consequently encourage the emergence of a monopoly and discipline the industry through regulated premiums. It is also shown that government intervention of last resort is not needed when the risks are highly correlated. Lastly, the results point out that when the risks between two regions are not sufficiently independent, the pooling of the risks can lead to a Pareto improvement only if the regions face similar magnitude of damage. If not, then the region with low-damage events needs the premium to decrease to accept the pooling of the risks.".

Rapide exposé dans le cadre d'une rencontre entre les économistes et les statisticiens rennais: glm, gam, gnm et données de panels.