The Sixth Spring School in Risk Management, Insurance, and Finance took place on March 23–25, 2017 at the Department of Economics at the European University at St. Petersburg. N. Göran Högnäs (Åbo Akademi University, Finland), Mario V. Wüthrich (ETH Zurich, Switzerland) and Antoon A. J. Pelsser (Maastricht University, the Netherlands) introduced the audience to such topics as «Introduction to Stochastic Demography», «New Developments in Claims Reserving», and «Replicating Portfolios for the Pricing and Risk Management of Insurance Liabilities».
March 23th, 2017
Introduction to Stochastic Demography
Professor N. Göran Högnäs, Åbo Akademi University, Finland
Göran Högnäs is Professor Emeritus of Applied Mathematics at Åbo Akademi University. He has played a central role in the probabilistic community in Finland as founding director of the national Finnish Graduate School in Stochastics and Statistics (1998–2009) and as organizer during many years of the Finnish Summer School on Probability Theory (currently in its 40th year!). He was responsible for the local organization of the Third Finnish-Soviet Symposium on Probability Theory and Mathematical Statistics, Turku 1991. His research interests are in probability theory on topological semigroups as well as Markov chain theory and stochastic population models. He is the coauthor, with Arunava Mukherjea, of the monograph Probability Measures on Semigroups. Convolution Products, Random Walks, and Random Matrices, 2nd ed. Springer 2011.
Professor Högnäs currently serves as associate editor of Journal of Theoretical Probability (1988 – ) and Journal of Difference Equations and Applications (2008 – ). He is a member of Societas Scientiarum Fennica (Finnish Society of Sciences and Letters, est. 1838) since 1997.
Summary of the Course
Demographic factors have a profound impact on our communities, influencing public policy decisions in all walks of life, from infancy to old age. It goes without saying that reliable demographic predictions are in great demand in the modern society. Particular concerns are future pensions and the design of nursing and health care services as well as other welfare benefits.
Mathematics and mathematical models have always played a fundamental role in demography. Very early, it became evident that sound mathematical ideas are vital to the success of insurance and pension schemes, even if the possibility of failure can never be disregarded since future events cannot be foreseen with certainty.
This course briefly traces the origins of demography from its start in the 17th century. Many of the basic notions are present in the thinking of those early pioneers.
Demography relies on the law of large numbers and mass action. Deterministic models provide a natural starting point for predictions. The efforts to predict the changes in demographic parameters (such as lower mortality and, especially, variations in fertility) have not been particularly successful.
Thus modern demographic forecasts are predominantly statistical, i.e., we rely on the future being an extension of the past and the present: plus ça change, plus c’est la même chose. The course concerns the mathematics of some of the major methods used and some ways in which the demographers have tried to measure their forecast errors.
Life tables, basic principles of demography
Classic deterministic models, Leslie matrix methods
Stochastic models, Lee–Carter approach
Juha M. Alho and Bruce D. Spencer. Statistical Demography and Forecasting, Springer Science+Business Media, 2006.
Nathan Keyfitz. Applied Mathematical Demography, John Wiley, 1977.
Nathan Keyfitz and Hal Caswell. Applied Mathematical Demography, 3rd ed., Springer Science+Business Media, 2005.
Marie-Claire Koissi, Arnold F. Shapiro and Göran Högnäs. Evaluating and extending the Lee–Carter model for mortality forecasting: bootstrap confidence interval, Insurance Math. Econom. 38 (2006), no. 1, pp. 1–20.
Ronald Lee. The Lee–Carter Method for Forecasting Mortality, with Various Extensions and Applications, North American Actuarial Journal, 4 (2000), no. 1, pp. 80–91.
Perspectives on Mortality Forecasting, II. Probabilistic Models, Nico Keilman (Ed.), Social Insurance Studies No. 2, Swedish Social Insurance Agency, 2005.
J. H. Pollard. Mathematical models for the growth of human populations, Cambridge University Press, 1973.
March 24th, 2017
New Developments in Claims Reserving
Professor Mario V. Wüthrich, ETH Zurich, Switzerland
Mario V. Wüthrich is Professor in the Department of Mathematics at ETH Zurich, Honorary Visiting Professor at City University London, Honorary Professor at University College London and Swiss Finance Institute Professor. He holds a PhD in Mathematics from ETH Zurich. From 2000 to 2005, he held an actuarial position at Winterthur Insurance and was responsible for claims reserving in non-life insurance, as well as developing and implementing the Swiss Solvency Test. He is fully qualified actuary SAA, serves on the board of the Swiss Association of Actuaries, and is editor of ASTIN Bulletin.
Summary of the Course
The claims reserves are the biggest position on the liability side of the balance sheet of a non-life insurance company. They have a big impact on profit and loss statements and they are a main risk driver in solvency considerations of non-life insurance companies. The aim of this course is to discuss this position and to analyse possible deviations in claims reserves arising from prediction errors. We consider the following 4 sections:
1) We present the classical chain-ladder model and provide Mack's (static) uncertainty formula.
2) We extend Mack's static uncertainty formula to a dynamic point of view. This includes in a first step the one-year uncertainty formula (Merz–Wüthrich formula), and in a second step the total run-off uncertainty analysis. The latter is useful for cost-of-capital considerations.
3) We give a brief introduction to regression trees, which is an estimation and calibration method used in machine learning and data analytics.
4) We present an application of machine learning methods to a claims reserving problem. This will provide claims reserves for individual claims.
1) Claims Run-Off Uncertainty: The Full Picture
2) Stochastic Claims Reserving Manual: Advances in Dynamic Modeling
3) Data Analytics for Non-Life Insurance Pricing
4) Machine Learning in Individual Claims Reserving
March 25th, 2017
Replicating Portfolios for the Pricing and Risk Management
of Insurance Liabilities
Professor Antoon A. J. Pelsser, Maastricht University, the Netherlands
Antoon Pelsser is working at Kleynen Consultants and is also a Full Professor of Finance and Actuarial Science at Maastricht University and a research fellow at Netspar. His academic research interests focus on pricing models for interest rate derivatives, the pricing of insurance contracts and Asset-Liability Management (ALM) for insurance companies. He previously held positions as Erasmus University in Rotterdam and the University of Amsterdam. He has published in leading academic journals including Journal of Economic Theory, Mathematical Finance, Finance and Stochastics, Insurance: Mathematics and Economics. He is an Honorary Fellow of the Institute of Actuaries.
Besides his academic career, he has also worked in the financial industry. From 2004 until 2007 he worked at ING Group's staff department Corporate Insurance Risk Management. There he was involved in implementing a new internal model for measuring Economic Capital for ING-Insurance. From 2000 until 2004 he worked as Head of ALM for Nationale-Nederlanden. Before that, he worked 7 years in the dealing-room of ABN-Amro Bank in Amsterdam, where he was responsible for the development of pricing models for derivatives.
Summary of the Course
Portfolio Replication methods have become increasingly important as risk management tools for insurance companies. The method of Replicating Portfolios allows insurance companies to calculate quickly and accurately the financial risks of (complete portfolios of) insurance liabilities. By mapping the existing liabilities onto Replicating Portfolios of traded financial instruments, significant improvements in speed and accuracy can be obtained compared to traditional methods such as model points or full Monte-Carlo simulation of the insurance liabilities. This course offers a hands-on introduction into the theory and implementation of Replicating Portfolios for insurance liabilities.
- Basic idea of Replicating Portfolios
- Theoretical Justification
- Comparison to alternative methods: function fitting
- Constructing Replicating Portfolios and Validation
- Using Replicating Portfolios for Risk Calculations
Partners and Supporters
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Photo Report of the School 2017
Photos can be downloaded here.