ASTIN Achievements – International Actuarial Association

Our Achievements and Prominent Figures

ASTIN’s main achievements consist in developing new research areas, introducing them to the actuarial profession and finding their meaningful practical application in the industry. The range of areas of focus is quite wide, stretching from classical risk theory, ratemaking and reserving to more contemporary quantitative risk and capital managements and newly emerging data science and machine learning. All these achievements would not be possible without a number of ASTIN’s prominent figures who make a significant contribution to the development of intellectual base of ASTIN at different times and epochs.

1900-1980

Filip Lundberg

Harald Cramér

Ingvar Sternberg

Gunnar Benktander

Teivo Pentikäinen

Paul Johansen

Bobby Beard

Edouard Franckx

Bruno de Finetti

Hans Ammeter

1960's-Today

Karl Borch

Hans Bülmann

Hans Gerber

Jean Lemaire

Marc Goovaerts

Harry Panjer

Paul Embrecths

Thomas Mack

Gregory Taylor

Gary Venter

This section provides a brief description of each of the areas of focus as well as a short biography of the prominent figures involved.

Risk Theory

Read Dubourdieu peu à peu. Read Beard et alia’s text. And what comes next? The many references appeal in this book by Hilary Seal. Hans Bühlmann, my thesis advisor, will make you even wiser. John Beekman’s first process concerns the risky business. John Wooddy in his notes from many sources quotes. Reading Borch’s tracts will not be futility to anyone who believes in utility. It should be stated that Wolff’s book is related. Is your probability sound? See Feller for background.

Hans Gerber

The theory of risk is the bedrock of actuarial science, and non-life actuarial science in particular. Its origin traces back to 1903, the year Swedish mathematician Filip Lundberg published his PhD thesis on Approximations of the Probability Function / Reinsurance of Collective Risks. In it, Filip Lundberg utilised the results of central limit theorem that was earlier formally stated and proved by Russian mathematician A. Lyapunov, and introduced the notion of Compound Poisson. This seminal work was ahead of its time and required another 30 years to be fully understood, appreciated and further developed to a complete theory.

Later, in the 1930s, another great mathematical mind from Sweden Professor Harald Cramér further developed Lundberg’s ideas by formalising them into ‘Collective Risk Theory’ and also linking them to the then emerging theory of stochastic processes.

The Cramér-Lundberg’s new Collective Risk Theory focuses mainly on the following two problems:

Finding the distribution of total claims cost at a fixed time; and
Computing the ruin probability of the insurance company with the stochastic process of surplus.

The concept of defining stability of insurance process through the level of ruin probability resonates with the principles underlying the reliability theory that is often used in engineering science.

An alternative view of insurance risk, taking a more economic view of profitability and pragmatic firm value, was later proposed by Italian mathematician and actuary Bruno de Finetti, and further developed by others. Bruno de Finetti defines the value of insurance company as the present value of future discounted dividends up to the ruin time and suggests maximising it. His idea was first presented in 1957 at the ICA in New York. This new way of thinking created a big shift in the paradigm, so big that the actuarial community was not ready to fully embrace it.

Later, Karl Borch and Hans Gerber, and other scholars, further developed de Finetti’s ideas and applied them to solving practical problems of risk theory. In particular, Karl Borch fully exploited de Finetti’s ideas in insurance economics, Hans Gerber further contributed by solving the problems of finding an optimal dividend pay-out and the distribution of surplus at ruin in the presence of dividends.

Today, various quantitative risk management methods of risk and capital optimisation are based on maximising the de Finetti’s value of the firm subject to solvency constraints. These type optimisations serve as dual optimisation problems to the minimisation of ruin probability subject to profitability. In such a way one could relate the de Finetti’s concept of pragmatic value of the firm to the engineers view of risk process and managing its stability via controlling the probability of ruin.

Further refinements of Cramér-Lundberg’s Collective Risk Theory are associated with the research work of the following well known individuals of the ASTIN community:

Ove Lundberg (son of Filip Lundberg) and Hans Ammeter – were independently advocating for flexing the frequency parameter in Compound Poisson loss, Poisson parameter, by making it random. Their approach gained popularity among practitioners. They could much easier adjust the risk model to the real data of an insurance company. This approach was propagated under the name Fluctuating Basic Probabilities.
Bobby Beard, Teivo Pentikäinen, Erkki Pesonen and Chris Daykin – were the first to generalise the insurance risk process by introducing experience rating and interest rate. With that generalisation the analytical mathematics reached its limits fairly quickly. The ideas of using computer simulations to perform dynamic financial analysis (DFA) of insurance risk process was born. This approach can be applied to any generalised (realistic) risk process. Today, computer simulation based DFA approach is used in risk and capital modelling to support the management in their strategic decision making.
Harry Panjer – finding the analytical way of computing the distribution of total (compound) loss in Cramér-Lundberg’s model was a formidable task. It was Harry Panjer who in 1980 showed how the problem could be solved by recursion. He triggered a whole new branch of practical research, the so called ‘risk theory numerics’. Thanks to this discovery, actuaries also learned from numerical analysts that another practical way of computing the distribution of total compound loss was to use the Fast Fourier Transform.
Hans Gerber – in 1973 he introduced martingales in risk theory. This was a remarkable initiative. Transforming the risk process into a martingale builds a direct link to mathematical finance.

Insurance Economics

This area is mainly associated with Professor Karl Borch, the great scholar and contributor to the intellectual base of ASTIN. Karl Borch taught us the theory of economics of uncertainty, ‘utility theory’, that was formulated in his famous book The Economics of Uncertainty. He introduced the economic concept of risk exchange (Fundamental Theorem of Borch) – his pioneering work on Pareto-optimal risk exchange in reinsurance opened a new area in actuarial science. He was also a big promoter of de Finetti’s ideas of maximising the value of the firm.

Karl Borch has never served on ASTIN Committee, but he was one of the most enthusiastic and influential members of ASTIN. No single person has contributed more to the columns of ASTIN Bulletin.

Karl Borch was also active in other professional insurance forums which activities are relevant to the work we do at ASTIN. In particular, he was a long-serving and active member of The Geneva Association – he was a driving force behind the maturation of this group.

Other areas

Credibility theory

The statistical concept of credibility has its origin in North America and traces back to 1918, the year when the seminal paper of A.W. Whitney on ‘credibility theory and its application to experience rating’ was published in the Proceedings of the Casualty Actuarial Society. The concept of credibility introduced by Whitney is often referred to as American credibility.

In Europe, Hans Bühlmann further developed this concept and introduced the new model, Bühlmann model or alternatively ‘variance component model’, which can be used to determine the appropriate premium for a group of insurance contracts. This model was further developed and evolved to the so called Bühlmann-Straub model, as the result of subsequent work done by Erwin Straub (PhD student of Hans Bühlmann).

Hans Bühlmann is a long-serving member of ASTIN and a great contributor. He was elected Honorary Chairman of ASTIN in 1995, after serving on the ASTIN Committee as Chairman (1973-74), Vice-Chairman (1971-72) and Chief Editor of ASTIN Bulletin (1985-1995).

The list of other great contributors to this area includes L.H. Longley-Cook (CAS) and Alois Gisler.

Risk Measures and Premium Calculation Principles

This area is associated with many interesting contributors, one individual who stands out is Marc Goovaerts. Marc Goovaerts was the first who systemised the principles of premium calculations in his book Insurance Premiums: Theory and Applications. He was also an authority in such areas as risk measures and their applications in risk and capital modelling.

Marc was an active member of ASTIN and one of the main contributors to the columns of ASTIN Bulletin.

He was also active in other professional actuarial forums. Along with Hans Gerber, Etienne De Vylder and Jean Haezendonck, he founded the Insurance: Mathematics and Economics (IME) - the forum of actuarial academics with research interest in risk theory and insurance mathematics and economics. For many years, he was the Chief Editor of the IME Journal.

Bonus-Malus

Jean Lemaire – the name we all familiar with when it comes to bonus-malus systems in automobile insurance. His research interests also extend to the areas of insurance economics and game theory.

He was elected Honorary Chairman of ASTIN in 2008, after serving ASTIN as Treasurer (1982-1997), Vice-Chairman (1998-2007) and Chairman (1985-1990 and 2002). His books on bonus-malus theory won book-of-the-year awards in Europe (The Geneva Association) and in the USA (American Risk and Insurance Association), and have been translated into French, Spanish, Russian, Korean, Japanese, and Mandarin. He has lectured in 86 countries.

Insurance Solvency

The risk theoretical concepts of insurance solvency and their practical applications were developed and introduced to actuarial profession in the late 1980s through the series of working groups and conferences on insurance solvency

The main contributors to these developments at the time from ASTIN’s side were:

Finland: Teivo Pentikäinen, Erkki Pesonen and Jukka Rantala;
Denmark: H. Ramlau-Hansen;
UK: Chris Daykin
Australia: Greg Taylor

Among those from outside ASTIN who made significant contribution were the following renowned insurance economists: Neil Doherty, H. Schlesinger, David Cummins and Richard Derrig.

Much later in 2000s with the emergence of Solvency II a lot of work was carried out to bring the theoretical concepts of insurance solvency into real applications. One individual from the ASTIN community of note is Arne Sandström. Arne is an active member of ASTIN. He was the first to systemise the concepts and quantitative methods of insurance solvency in his book titled ‘Handbook of Solvency for Actuaries and Risk Managers’.

Reserving

This area resonates with a few prominent figures that are well known to ASTIN community and the wider non-life actuarial audience:

Thomas Mack – developed the famous ‘Mack model’ that is used to derive the non-parametric statistical estimate of reserve variability. Thomas is an active member of ASTIN and a great contributor to the columns of ASTIN Bulletin.
Greg Taylor – active member of ASTIN and a great contributor to the columns of ASTIN Bulletin. His research mainly focuses on the problems of stochastic reserving. He has published a book on actuarial methods of loss reserving.
Glenn Meyers – active member of ASTIN and a regular contributor to the columns of ASTIN Bulletin. He served on ASTIN Committee. In his research he has been mainly focussing on the problems of stochastic reserving, including those that are based on Markov Chain Monte Carlo Chain Ladder methods.
Gary Venter – active member of ASTIN and a regular contributor to the columns of ASTIN Bulletin. In his research one of his main areas of focus is stochastic reserving. He has also been active in doing research in reinsurance, dependence modelling, risk measures and capital allocation.
Mario Wüthrich – active member of ASTIN, currently serves as Chief Editor of ASTIN Bulletin. His research mainly focusses on the problems of stochastic reserving. He has recently developed the so called Merz-Wüthrich model for estimating the reserve risk over a one-year time horizon. This model has gained much popularity, especially after the implementation of Solvency II regime in Europe and the UK.

Quantitative Risk Management (QRM)

This is the large contemporary area of actuarial science comprising the following concepts and techniques:

Risk measures
Financial time series
Multivariate modelling: Copulas and Dependence
Risk aggregation
Operational risk modelling
Extreme Value Theory and catastrophe modelling
Model risk
Advanced Insurance Analytics

The driving force behind the QRM advances in actuarial profession is Paul Embrechts. Paul is Professor at ETH, Zurich and also the founder and leader of the well-known risk and actuarial think-tank RiskLab. He is an active member of ASTIN and its great contributor and has been regularly addressing at ASTIN colloquia as a keynote speaker. Paul served as Chief Editor of ASTIN Bulletin [1996-2005]. He is well known for his extensive research publications and also for his books on Quantitative Risk Management and Extreme Value Theory.