Search

The loss count distributions whose probabilities ultimately satisfy Panjer’s recursion were classified between 1981 and 2002; they split into six types, which look quite diverse. Yet, the distributions are closely related – we show that their probabilities emerge out of one formula: the binomial series. We propose a parameter change that leads to a unified, practical and intuitive, representation of the Panjer distributions and their parameter space. We determine the subsets of the parameter space where the probabilities are continuous functions of the parameters. Finally, we give an inventory of parameterisations used for Panjer distributions.

This paper looks at fundamental findings from the field of empirical intercultural research, taking an unusual viewpoint: analogies with insurance premium rating. Intercultural findings are of interest to the insurance industry in their own right. They become even more interesting, however, when viewed through the eyes of an actuary who applies advanced statistics to big data sets and, in doing so, has to tackle challenges similar to those faced by cross-cultural researchers: complex data, many random effects and the desire to interpret statistics intuitively, yet still remain as objective as possible. If one views the results of intercultural research with the same pragmatism as one would the premium rating outputs of e.g. GLMs – i.e. being neither overly sceptical about the models nor trusting them blindly – one realises they can serve as a helpful source of inspiration for the day-to-day work.

The classical way to get an analytical model for the (supposedly heavy) tail of a loss severity distribution is via parameter inference from empirical large losses. However, in the insurance practice it occurs that one has much less information, but nevertheless needs such a model, say for reinsurance pricing or capital modeling. We use the Generalized Pareto distribution to build consistent underlying models from very scarce data like: the frequencies at three thresholds, the risk premiums of three layers, or a mixture of both. It turns out that for typical real-world data situations such GPD “fits” exist and are unique. We also provide a scheme enabling practitioners to construct reasonable models in situations where one has even less, or somewhat more, than three such bits of information. Finally, we have a look at model risk, by applying some parameter-free inequalities for distribution tails and a particular representation for loss count distributions. It turns out that, in the data situation given above, the uncertainty about the severity can be surprisingly low, such that the overall uncertainty is driven by the loss count.

We see language in a purely technical way: as sending and receiving complex signals. A signal can be understood to mean a sound, but also, for example, a term. In different languages, the signals used are partly different or different in importance. Unfortunately, this is not general knowledge. Ignorance of the essential signals of a foreign language that one is learning leads to mistakes of which one is not aware and thus to rather inefficient learning. This can be remedied by consciously dealing with the relevant signals of your own and the foreign language and making yourself aware of the differences.

In insurance and even more in reinsurance it occurs that about a risk you only know that it has suffered no losses in the past e.g. seven years. Some of these risks are furthermore such particular or novel that there are no similar risks to infer the loss frequency from. In this paper we propose a loss frequency estimator that copes with such situations, by just relying on the information coming from the risk itself: the “amended sample mean”. It is derived from a number of practice-oriented first principles and turns out to have desirable statistical properties. Some variants are possible, which enables insurers to align the method to their preferred business strategy, by trading off between low initial premiums for new business and moderate premium increases for renewal business after a loss. We further give examples where it is possible to assess the average loss from some market or portfolio information, such that overall one has an estimator of the risk premium.

The financial crisis of 2007 has triggered various debates, ranging from the stability of the banking system to subtle technical issues regarding the Gaussian and other copulas. All these debates are important, and it might be good to start even a further one: Credit derivatives have much in common with treaty reinsurance, e.g. risk transfer via pooling and layering, scarce data, skewed distributions, and a limited number of specialized players in the market. All this leads to a very particular mixture of mathematical/statistical and behavioral challenges. Reinsurers have been struggling to cope with these, not always successfully, but they have learnt many lessons during their more-than-one century in business. This has led to certain rules adopted by the reinsurance market and to a certain mindset adopted by the individuals working in the industry. Some of the traditions established in the insurance and reinsurance world could possibly inspire markets like the credit derivatives market.

Modern society mitigates and transfers risks in a variety of ways, which range from catastrophe prevention and insurance solutions through to injustices of a minor and inconspicuous nature. We illustrate that the measures taken depend on the uncertainty about the risks in question, and involve three trade-offs: innovation vs. risk avoidance; liability vs. collective risk sharing; and equity vs. practicable claims settlement. We study two highly instructive examples: nuclear liability and the measures taken in the wake of the 9/11 terrorist attack.

Fitting loss distributions in insurance is sometimes a dilemma: either you get a good fit for the small/medium losses or for the very large losses. To be able to get both at the same time, this paper studies generalizations and extensions of the Pareto distribution. This leads not only to a classification of potentially suitable, piecewise defined, distribution functions, but also to new insights into tail behavior and exposure rating.

A myocardial bridge has traditionally been considered a benign condition characterized by an atypical intramyocardial route of a segment of one of the major coronary arteries. However, the clinical complications of myocardial bridges can be dangerous. These potential complications include acute coronary syndromes, arrhythmias, ventricular dysfunction, and sudden death. Myocardial bridges are suspected to be adjuvant of Kounis syndrome, which is defined as an acute coronary syndrome caused by an allergic reaction. Due to high epidemiologic prevalence, clinical suspicion of a myocardial bridge should be considered in atypical and typical presentations of chest pain, especially in patients with low-risk factors for atherosclerotic disease. A male in their late 30’s presented with non-ST elevation myocardial infarction suspected to be secondary to Kounis syndrome after gadobenate dimeglumine contrast media was used for an imaging study. His clinical presentation was further complicated when he was found to have a mid-left anterior descending coronary artery myocardial bridge.

The well-known inflation-independent exposure rating curves from Property reinsurance (see e.g. Mack (1980) or Bernegger (1997)) cannot be deduced in Liability insurance in the same way because here the claims sizes cannot be assumed to be scaled by the sums insured. Instead, German insurance and reinsurance companies apply a specific system of increased limits factors introduced already in 1936 by the pioneer of German non-life insurance mathematics, Paul Riebesell.