White papers

A Reacfin White Paper in Non-Life:

Posted on 20-09-2017

Machine Learning applications to non-life pricing

Frequency modelling: An educational case study

by Julien Antunes Mendes, Sébastien de Valeriola, Samuel Mahy and Xavier Maréchal

Machine Learning techniques operate data to perform classification and prediction. They are becoming more and more popular, due (among other things) to the still increasing computational power of machines. These algorithms use a very limited set of assumptions, compared to “standard” statistical methods. However, on the contrary of such methods, inference is not the main goal of Machine Learning techniques: they focus on classification and prediction. This is the reason why these “innovative” techniques are considered as more “black box” solutions.

This paper presents a comparison on a simulated database between traditional statistical predictive modelling techniques (GLM and GAM), machine learning techniques (regression trees, bagging, random forests, boosting and neural networks) and penalized regression techniques (Lasso, Ridge and Elastic Net).

Mortality projections for Belgium, general population over 1950–2015, with corrections for adverse selection

Posted on 27-05-2017

Lee-Carter modelling and adaptation to insurance mortality using Reacfin’s tools Thanatos and Hygie

by Elena Atienza Y Rubio, Michel Denuit, Julien Trufin et Julien Antunes Mendes

In most industrialized countries, including Belgium, mortality at adult and old ages reveal decreasing annual death probabilities. The calculation of expected present values (for pricing or reserving) for long-term survival insurance benefits thus requires an appropriate mortality projection in order to avoid underestimation of future costs. The so-called

projected life tables include a forecast of the future trends of mortality. This paper updates previous projections based on recent mortality statistics, for the general population and for the insurance market. A discussion of the strategies to deal with the systematic longevity risk concludes the study.

A Reacfin White Paper on Worker’s Compensation Insurance

Posted on 05-02-2017

A Unified Approach for the Modeling of Rating Factors in Workers’ Compensation Insurance

by Ben Stassen, Michel Denuit, Samuel Mahy, Xavier Maréchal and Julien Trufin

Workers’ Compensation is an insurance cover whereby an employer compensates for the lost wages and medical expenses of an employee who is injured on the job. As with other types of insurance, premium rates for workers' compensation policies are calculated according to several different factors. In Belgium, current market practice consists of pricing workers’ compensation based on a hierarchical credibility model, i.e. the Jewell model. Hierarchical credibility models provide a nice hierarchical procedure in the calculation of premiums. First, we produce an expected aggregate claim amount for the whole line of business. Then, we distribute this amount over lower levels (top down approach).

In this paper, we define a new tariff structure for workers’ compensation by combining hierarchical credibility models with a GLMM approach in the final pure premium model. We start with the calculation of a basic pure premium rate in function of some explanatory variables by using a Generalized Linear Mixed Model (which is an extension of the well-known Generalized Linear Models). The advantage of such a model is that we can now fit ordinary rating factors and hierarchical rating factors at the same time. Afterwards, this basic premium rate is adapted according to the client’s history of claims data with the use the Bühlmann-Straub credibility model.

Research in Actuarial Science: Compositions of Conditional Risk Measures and Solvency Capital

Posted on 23-01-2017

Compositions of Conditional Risk Measures and Solvency Capital 

Reacfin’s consultant, Dr. Adrien Lebègue, together with our chairman, Pr. Pierre de Volder, have just published a scientific article that proposes routes considering time-consistent risk measures to determine the necessary capital of pension funds or insurance companies.

In this paper, the authors consider compositions of conditional risk measures in order to obtain time-consistent dynamic risk measures and determine the solvency capital of a life insurer selling pension liabilities or a pension fund with a single cash-flow at maturity. Pr. Devolder and Dr. Lebègue first recall the notion of conditional, dynamic and time-consistent risk measures. They link the latter with its iterated property, which gives a way to construct time-consistent dynamic risk measures from a backward iteration scheme with the composition of conditional risk measures. They then consider particular cases with the conditional version of the value at risk, tail value at risk and conditional expectation measures. Finally, the authors give an application of these measures with the determination of the solvency capital of a pension liability, which offers a fixed guaranteed rate without any intermediate cash-flow.

This paper entitled “Compositions of Conditional Risk Measures and Solvency Capital” is currently available on the site of the Multidisciplinary Digital Publishing Institute here.

Research in Actuarial Science: Minimum Protection in DC Funding Pension Plans and Margrabe Options

Posted on 19-01-2017

New Scientific Paper: Minimum Protection in DC Funding Pension Plans and Margrabe Options

In the context of their academic research, our chairman, Professor Pierre Devolder, together with Reacfin’s senior consultant Dr. Sébastien de Valeriola, recently published a scientific paper regarding the valuation of pension plan features.

In Belgium a recent law change allows employers to choose between two different types of guarantees to offer to their affiliates. In this paper, the authors address the question arising naturally: which of the two guarantees is the best one? In order to answer that question, they set up a stochastic model and use financial pricing tools to compare the methods. More specifically, they link the pension liabilities to a portfolio of financial assets and compute the price of exchange options through the Margrabe formula.

This paper entitled “Minimum Protection in DC Funding Pension Plans and Margrabe Options” is currently available on the site of the Multidisciplinary Digital Publishing Institute here

AML: Market practices and upcoming risk solutions

Posted on 31-10-2016

Risk-Based Approach & examples of Machine Learning Application

By François Ducuroir and Maciej Sterzynski

On 27 and 28th of October 2016, the Union of Arab Banks held, in Beirut, its annual forum for heads of AML/CFT* compliance units.
At this occasion, Reacfin’s managing partners, François Ducuroir and Maciej Sterzynski, presented our experience with regard to current market practices and upcoming solutions in this matter.

Among other we discussed:

  • practical aspects of idesigning and deploying Risk-Based solutions for Anti-Money Laundering purposes, and
  • hands-on examples for using Machine Learning algorithms (i.e. Artificial Intelligence techniques) to identify relevant variables for an efficient identification of supiscious Money Laundering or Terrorism Financing behaviors.

Interested readers will find here the slides of this presentation:

Reacfin White Paper - Prospective Life Tables

Posted on 17-09-2016

An introduction to time‐dependent mortality models

by Julien Antunes Mendes and Christophe Pochet


Life expectancy at birth among early humans was likely to be about 20 to 30 years. It rose to between 40 and 45 by the middle of the 19th century. Rapid improvements began at the end of the 19th century, so that by the middle of the 20th century it was approximately 60 to 65 years. At the beginning of the 21st century, life expectancy at birth reached about 70 years. Two trends dominated the mortality decline:

The first half of the 20th century saw significant improvements in the mortality of infants and children (and their mothers).

Since the middle of the 20th century, gains in life expectancy have been mainly due to medical factors that have reduced mortality among older persons (reductions in deaths due to the “big three” killers – cardiovascular disease, cancer and strokes).

More in the pdf document.

A reacfin White Paper on Mortality

Posted on 17-09-2016

Adverse selection in lifetables models, Methods & applications

By Aurélie Miller and Julien Antunes Mendes

In many different applications (Solvency Capital Requirement, Best Estimate of Liabilities computation, Economic Balance Sheet statement, insurance products pricing, profit analysis…), insurance companies use lifetables to model the probability of death or survival.

Adverse selection is the fact that, depending on the features of the insurance products underwritten, policyholders could present different behavioral or health characteristics. This could lead to observe different death probabilities between policyholders of the same age among the different products. For Valuation and Risk Management purposes, as this difference could be large, it should therefore be accounted for.

The lifetables will thus be different for some segments of insurance policyholders and will be different from the general population mortality (of a country for example). By using adapted life tables, the insurance company can take into account the adverse selection.

Calibration of such tables will be based on a trade-off between appropriateness (specific features of the policyholders adequately captured) and accuracy (sufficient volume of data to obtain reliable parameters).

More in the pdf document.

A Reacfin White Paper on Life Insurance

Posted on 07-07-2016

Lapse rate models in life insurance and a practical method to foresee Interest Rates dependencies

Lapse rate modelling is an important topic for life insurers. Changes in such lapse rate can potentially lead to material losses or to liquidity problems. Yet lapses prove difficult to model because they can be influenced by large number of parameters including the policyholder’s behavioral characteristics, the product’s specificities or the financial markets and macro-economic environment.

Specifically the modeling of interest rate dependency proves both critical (as lapses could be driven by increasing interest rates) and difficult to calibrate (historical data offer for instance limited information as rates decreased almost continuously over the recent decades). In this white paper, our consultants Julie Zians, Aurélie Miller and François Ducuroir review market practices in the Belgian market with regard to the modeling of lapses. They further propose a pragmatic way to model and calibrate the interest rate dependency of lapse rates.

A Reacfin White Paper on Artificial Intelligence applications to Finance

Posted on 22-06-2016

Introduction to Machine Learning techniques used in the financial industry and a practical case study

By Arnaud Deltour and François Ducuroir

Machine Learning (“ML”) techniques, a sub-field of Artificial Intelligence, become increasingly popular within the financial industry to tackle issues involving large amounts of data.

In this paper we aim at providing the reader with a basic introduction to key ML concepts and techniques, explain how such approaches differ from the more traditional statistical analysis approach and illustrate this theoretical presentation with some simple yet very practical application within the financial industry.

We also illustrate our point with a case-study: a practical application of decision trees to build predictive LGD models in loan books management.
We wrap-up this paper with a high-level comparison between traditional statistical inference methods and ML techniques.