Tail Risk Measurement: Estimation, Sensitivity, Uncertainty

Introduction & Programme

Regulatory frameworks such as Solvency II require non-life insurers to quantify extreme risks — most notably the 99.5% Value-at-Risk over a one-year horizon for the Solvency Capital Requirement (SCR). In practice, however, this poses a fundamental challenge: historical loss data contains little to no information about such rare events, making direct estimation inherently unreliable.

This web session addresses exactly this gap. It provides participants with a structured and practical toolkit to estimate high-confidence risk measures from limited data — and, crucially, to understand and communicate the uncertainty involved, enabling more robust risk quantification, particularly in contexts such as SCR validation and ORSA.

Starting with classical parametric approaches and kernel density estimation, the course progresses to Extreme Value Theory (EVT), with a focus on the Peaks-over-Threshold (POT) method and the Generalised Pareto Distribution (GPD). Particular attention is given to threshold selection and to Bayesian formulations in which the threshold is treated as an uncertain parameter, enabling posterior-predictive inference for high quantiles. We also consider flexible bulk-tail mixture models that combine non-parametric bulk estimation with an EVT-based tail component.

For each method, the course takes a structured perspective across four dimensions:

• the point estimator and its finite-sample properties,
• parameter uncertainty and confidence intervals,
• sensitivity to modelling assumptions, and
• overall model uncertainty.

Finally, we connect tail risk modelling to practical risk steering by linking estimated risk measures to capital allocation via the Euler (gradient) principle, enabling a decomposition into marginal risk contributions across business units or risk types.

For the core methods, participants apply estimation procedures in hands-on R exercises using real non-life insurance loss data, developing both technical proficiency and the critical judgement required to interpret results.

Preliminary Programme
Friday, 12 February 2027
09:30-11:00 Estimating Aggregate Tail Risk
11:00-11:30 Break
11:30-13:00 Estimation Stability, Sensitivity, and Allocation

All the above times are given in CET (Central European Time).

Learning Objectives & Approach

The course provides a critical overview of methods for estimating tail risk at high confidence levels under real-world data constraints, examining where and why they differ in their conclusions.

R exercises on real non-life insurance data illustrate the methods in practice, with particular attention to the interpretation and limitations of the resulting estimates.

Participants

This web session is particularly intended for actuaries involved in enterprise risk management, risk communication, insurance pricing, business support or strategic decision making.

As we will be diving into an explicit case study implemented in R, you should bring a basic knowledge of the R programming language (https://www.r-project.org/) and RStudio.

Technical Requirements
Both R and RStudio need to be installed prior to attending the web session in order to participate effectively in the case study.

Please check with your IT department if your firewall and computer settings support web session participation (the programme Zoom will be used for this online training). Please also make sure to join the web session with a stable internet connection.

Lecturers

Dr. Philipp Aigner
Philipp holds a degree in mathematics and works as a consultant specializing in risk management in the insurance industry for Deloitte. His doctorate, completed in 2023 at Johannes Gutenberg University Mainz, focused on capital allocation methods and their application to practical issues. For his research, he was awarded the GAUSS Young Talent Award 2023 by the German Society for Insurance and Financial Mathematics (DGVFM) and the German Association of Actuaries (DAV).

Prof. Dr. Sebastian Schlütter
Sebastian studied business mathematics at the University of Ulm and holds a doctorate in business administration from the Goethe University Frankfurt, where he is a fellow at the International Center for Insurance Regulation (ICIR). He is a certified actuary of the German Association of Actuaries and has been working on Solvency II and Enterprise Risk Management for five years, partly in consulting and partly in the insurance industry. Since 2015, he is Professor of Quantitative Methods at the School of Business of Mainz University of Applied Sciences.

Language & CPD Credits

The language of the web session will be English.

CPD Credits
For this web session, the following CPD credits are available under the CPD scheme of the relevant national actuarial association:

• Austria: 3 points
• Belgium: 3 points
• Bulgaria: 4.5 points
• Croatia: individual accreditation
• Czechia: 3 hours
• Denmark: 3 credits
• Estonia: 3 hours
• Finland: 3 points
• France: 18 points
• Germany: 3 hours
• Greece: 4 points
• Hungary: 3 hours
• Iceland: 3 credits
• Ireland: 3 hours
• Italy: GdLA individual accreditation
• Latvia: 3 hours
• Lithuania: 3 hours
• Netherlands: approx. 3 points (individual accreditation)
• Norway: 3 points
• Poland: 3 hours
• Portugal: 3 hours
• Serbia: 3 hours
• Slovakia: individual accreditation
• Slovenia: individual accreditation
• Spain: CAC: 3 hours, IAE: 3 hours
• Switzerland: individual accreditation
• USA: SOA (Section B): up to 3.6 hours

No responsibility is taken for the accuracy of this information.

Fees & Registration Details

Early Bird Registration Fee (until 1 January 2027):

• For private customers in the EU: €240.00 + VAT of the billing country (example Germany: €285.60 incl. 19% VAT)
• For private customers outside the EU: €285.60 (incl. 19% VAT)
• For businesses within the EU (excl. Germany, with valid VAT ID): €240.00 (net, reverse charge applies)
• For businesses in Germany: €285.60 (incl. 19% VAT)

Regular Registration Fee (from 2 January 2027):

• For private customers in the EU: €315.00 + VAT of the billing country (example Germany: €374.85 incl. 19% VAT)
• For private customers outside the EU: €374.85 (incl. 19% VAT)
• For businesses within the EU (excl. Germany, with valid VAT ID): €315.00 (net, reverse charge applies)
• For businesses in Germany: €374.85 (incl. 19% VAT)
  

Important VAT Information:

• For private customers with a billing address in an EU country: VAT will be charged at the applicable rate in the country of the billing address. The final amount, including VAT, will be calculated upon invoicing.
• For customers with a non-EU (third country) billing address: Only a non-company billing address is accepted for VAT compliance reasons. 19% VAT applies to all non-EU private customers.
• For businesses within the EU (excluding Germany), Iceland, Liechtenstein, Norway, Switzerland, and the UK with a valid VAT ID: The reverse charge mechanism applies (net price; VAT will not be charged). Please ensure your valid VAT ID is entered correctly during registration.
• For all customers with a billing address in Germany: 19% VAT applies.

Please submit your registration using our online form below. Closer to the event, you will receive further login details to join the web session.

Your registration is binding. Cancellation is only possible up to 2 weeks before the first day of the event. If you cancel later, the full participation fee is due. You may appoint someone to take your place but must notify us in advance. EAA has the right to cancel the event if the minimum number of participants is not reached.

We will send you an invoice via email. Please allow a few days for handling. Please always give your invoice number when you effect payment. All bank charges are to be borne by the participant.

Registration is open until two working days before the web session. If registration has already been closed for this web session, please call us or send an email to contact@actuarial-academy.com in order to find out whether a late registration is still possible.