The SCOR Papers are a collection of scientific articles published by SCOR on issues linked to risk and insurance.
#39 | December 2016
A General Framework for Modeling Mortality to Better Estimate its Relationship to Interest Rate Risks
Michel Dacorogna and Giovanna Apicella
The need for having a good knowledge of the degree of dependence between various risks is fundamental for understanding their real impacts and consequences, since dependence reduces the possibility to diversify the risks. This paper expands in a more theoretical approach the methodology developed in  for exploring the dependence between mortality and market risks in case of stress. In particular, we investigate, using the Feller process, the relationship between mortality and interest rate risks. These are the primary sources of risk for life (re)insurance companies. We apply the Feller process to both mortality and interest rate intensities. Our study cover both the short and the long-term interest rates (3m and 10y) as well as the mortality indices of ten developed countries and extending over the same time horizon. Specifically, this paper deals with the stochastic modelling of mortality. We calibrate two different specifications of the Feller process (a two-parameters Feller process and a three-parameters one) to the survival probabilities of the generation of males born in 1940 in ten developed countries. Looking simultaneously at different countries gives us the possibility to find regularities that go beyond one particular case and are general enough to gain more confidence in the results. The calibration provides in most of the cases a very good fit to the data extrapolated from the mortality tables. On the basis of the principle of parsimony, we choose the two-parameters Feller process, namely the hypothesis with the fewer assumptions. These results provide the basis to study the dynamics of both risks and their dependence.
#38 | April 2016
Explicit diversification benefit for dependent risks
Michel Dacorogna, Laila Elbahtouri and Marie Kratz
We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence.
#37 | March 2016
ALM Model: The contribution of Fuzzy Logic to behaviour modelling
Sylvain Detroulleau and Sandrine Mouret
The reforms ushered in by Solvency 2 introduce a new method for the valuation of insurance company balance sheets. The principle of “fair value” is now used to measure assets and liabilities: asset values are calculated at market value, while for liabilities the Best Estimate method is used. In life insurance and, more specifically, in the life insurance savings segment, it is necessary to model all possible interactions between the asset portfolio and the portfolio of liabilities. ALM (Asset Liability Management) models seek to forecast all of these interactions by integrating – over and above the usual financial and technical assumptions – assumptions pertaining to the behaviour of both policyholders and management. These behavioural laws, such as the laws governing policy surrender, for policyholders, and the policy governing credited interest rates, for management, can lead to problems in terms of their calibration, their modelling and, more broadly, their justification.
Given the decisive impact of behavioural laws when it comes to establishing Best Estimate values for liabilities, the objective of our study is to propose an alternative to the modelling of behavioural laws that is traditionally implemented within ALM models. The focus of our interest is a theory founded on human logic that has been widely tried and tested in other sectors of activity, such as manufacturing and heavy industry: fuzzy logic.
In the course of our study, we use fuzzy logic to model the behaviour of policyholders when it comes to economic lapses and that of insurers when it comes to the target rate credited to policyholders. The model we have built allows us to end up with a quantified decision while also simulating a human thinking process where the criteria are expressed in linguistic ways. Our results are encouraging. We demonstrate that the fuzzy approach allows us both to justify and generalize the ACPR’s economic surrenders function and that a fuzzy modelling of the policy governing credited interest rates allies optimization and an accurate representation of management’s policy.
#36 | February 2016
Spatial Risk Measures and Applications to Max-Stable Processes
The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from environmental events into the measure of the risk. We develop a new concept of spatial risk measure, based on the spatially aggregated loss over the region of interest, and propose an adapted set of axioms which quantify the sensitivity of the risk measure with respect to space and are linked to spatial diversification in particular. In order to model the loss underlying our definition of spatial risk measure, we apply a damage function to the environmental variable considered. In our examples, the latter is assumed to follow a max-stable process, very well suited to the modeling of extreme spatial events. The damage function considered is adapted to heatwaves. The theoretical properties of the resulting examples of spatial risk measures are studied and some interpretations in terms of insurance are provided.
#35 | January 2016
The Globalization of Infectious Diseases
Stephen Morse and Patrick Zylbermann
In a globalized world with rapidly evolving ways of life, the monitoring of emerging infectious diseases is becoming even more important. Recent epidemics, such as HIV/AIDS, SARS and H1N1, highlight patterns of emergence and propagation that will likely be repeated. Only strict monitoring and strong action can help to prevent the occurrence of an event such as the 1918 flu.
#34 | November 2015
A Change of Paradigm for the Insurance Industry
#33 | April 2015
Exploring the Dependence between Mortality and Market Risks
Michel Dacorogna and Meitner Cadena
#32 | March 2015
An Integrated Notional Defined Contribution (NDC) Pension Scheme with Retirement and Permanent Disability
Manuel Ventura-Marco and Carlos Vidal-Meliá
#31 | January 2015
The use of economic scenarios generators in unstable economic periods
#30 | September 2014
Explicit Föllmer-Schweizer decomposition of life insurance liabilities through Malliavin calculus
Sébastien de Valeriola
#29 | September 2014
A game-theoretic approach to non-life insurance market cycles
#28 | September 2014
Solar storms and their impacts on power grids Recommendations for (re)insurers
#27 | Octobre 2013
Are great earthquakes clustered?
#26 | September 2013
The risk-free rate: an inescapable concept?
Michel Dacorogna and Jérôme Coulon
#25 | July 2013
Financial Valuation in a Volatile Scenario of the Guaranteed Minimum Withdrawal Benefit (GMWB) Policy
#24 | May 2013
Does risk diversification always work? The answer through simple modelling
Marc Busse, Michel Dacorogna and Marie Kratz
#23 | May 2013
A new Dividend Strategy in the Brownian Risk Model
#22 | April 2013
Non-Life Insurance Market Growth in China: Can we predict it?
#21 | February 2013
Surrender analysis in a segregated fund
#20 | June 2012
How Long Will We Live? A Demographer’s Reflexions on Longevity
James W. Vaupel
#19 | May 2012
Microscopic longevity modeling and its practical applications
#18 | March 2012
Market Value Margin: Practical calculations under the Solvency II Cost of Capital approach
#17 | October 2011
EU regulation of greenhouse gas emissions: what solutions can insurance companies offer industry?
#16 | June 2011
A new method for modeling dependence via extended common shock type model
#15 | May 2011
Why do the French not purchase more long-term care cover?
EN | FR
#14 | April 2011
Modelling operational risk in the insurance industry
EN | FR
#13 | March 2011
Preparing for Solvency II: Points of debate in the Standard Formula
Michel M. Dacorogna, Ecaterina Nisipasu and Mathieu Poulin
#12 | December 2010
Study of the impact of inflation and GDP growth on property-liability and life insurance premiums over the last 30 years: case of the G7 countries
EN | FR
#10 | December 2010
PrObEx: A new method for the calibration of copula parameters from prior information, observations and expert opinions
Philipp Arbenz and Davide Canestraro
#8 | March 2010
Principle-based solvency: A comparison between Solvency II and the Swiss Solvency Test
Michel Dacorogna and Philippe Keller
#7 | March 2010
The Influence of Risk Measures and Tail Dependencies on Capital Allocation
Michel Dacorogna and Davide Canestraro
#6 | January 2010
Adapting the solvency regulations to times of crisis, accepting the riskiness of the situation
Jean-Luc Besson, Michel Dacorogna and Philippe Trainar
EN | FR | DE
#5 | July 2009
Securitization, Insurance and Reinsurance
J. David Cummins and Philippe Trainar
#4 | March 2009
Modern companies and extreme risks
#2 | August 2008
La bancassurance généralisation ou déclin du modèle ?
#1 | September 2008
Using Capital Allocation to Steer the Portfolio towards Profitability
Jean-Luc Besson, Michel Dacorogna, Paolo de Martin, Michael Kastenholz and Michael Moller
EN | FR | DE
From Principle Based Risk Management to Solvency Requirements
SCOR has traditionally been a strong proponent of advanced risk management methods and models in the insurance industry.
In the book “From Principle-based Risk Management to Solvency Requirements", SCOR specialists describe over five hundred pages how the company models risks according to the requirements of the Swiss Solvency Test (SST), which is based on concepts very similar to the ones set forth by Solvency II.
Beyond the regulatory requirements, the understanding of the concepts involved as well as the results of the comprehensive risk modelling process are essential in all sectors and are vital to the development of a coherent Enterprise Risk Management (ERM) process.
The understanding of the ERM process allows companies to optimally allocate the capital necessary for their business and to devise a comprehensive, successful and coherent risk strategy.
SCOR is happy and proud to share its state-of-the-art modelling approach with different communities: academic, regulators, actuaries, clients and other interested parties.