Bayesian Methods in Insurance Companies´ Risk Management



By Anne Puustelli
January 2012
Tampere University Press
Distributed by Coronet Books Inc.

ISBN: 9789514486357
122 pages

$87.50 Paper original


In this thesis special issues emerging from insurance companies' risk management are considered in four research articles and in a brief introduction to concepts examined in the articles. The three main topics in the thesis are financial guarantee insurance, equity-linked life insurance contracts, and mortality modeling.

Common to all of the articles is the utilization of Bayesian methods. With these the model and parameter uncertainty can be taken into account. As demonstrated in this thesis, oversimplified models or oversimplified assumptions may cause catastrophic losses for an insurance company. As financial systems become more complex, risk management needs to develop at the same time. Thus, model complexity cannot be avoided if the true magnitude of the risks the insurer faces is to be revealed. The Bayesian approach provides a means to systematically manage complexity.

The topics studied here serve a need arising from the new regulatory framework for the European Union insurance industry, known as Solvency II. When Solvency II is implemented, insurance companies are required to hold capital not only against insurance liabilities but also against, for example, market and credit risk. These two risks are closely studied in this thesis. Solvency II also creates a need to develop new types of products, as the structure of capital reguirements will change. In Solvency II insurers are encouraged to measure and manage their risks based on internal models, which will become valuable tools. In all, the product development and modeling needs caused by Solvency II were the main motivation for this thesis.

In the first article the losses ensuing from the financial guarantee system of the Finnish statutory pension scheme are modeled. In particular, in the model framework the occurrence of an economic depression is taken into account, as losses may be devastating during such a period. Simulation results show that the required amount of risk capital is high, even though depressions are an infrequent phenomenon.

In the second and third articles a Bayesian approach to market-consistent valuation and hedging of equity-linked life insurance contracts is introduced. The framework is assumed to be fairly general, allowing a search for new insurance savings products which offer guarantees and certainty but in a capital-efficient manner. The model framework includes interest rate, volatility and jumps in the asset dynamics to be stochastic, and stochastic mortality is also incorporated. Our empirical results support the use of elaborated instead of stylized models for asset dynamics in practical applications.

In the fourth article a new method for two-dimensional mortality modeling is proposed. The approach smoothes the data set in the dimensions of cohort and age using Bayesian smoothing splines. To assess the fit and plausibility of our models we carry out model checks by introducing appropriate test quantities.

Acta Universitatis Tamperensis No. 1681

 

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