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Economic Factors and Solvency

Published online by Cambridge University Press:  09 August 2013

Harri Nyrhinen
Harri Nyrhinen*
Affiliation:
Department of Mathematics and Statistics, P.O.Box 68 (Gustaf Hällströmin Katu 2b), FIN 00014, University of Helsinki, Finland, E-mail: [email protected]
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Abstract

We study solvency of insurers in a practical model where in addition to basic insurance claims and premiums, economic factors like inflation, real growth and returns on the investments affect the capital developments of the companies. The objective is to give qualitative descriptions of risks by means of crude estimates for finite time ruin probabilities. In our setup, the economic factors have a dominant role in the estimates. In addition to this theoretical view, we will focus on applied interpretations of the results by means of discussions and examples.

The first version of the paper was presented in ASTIN Colloquium in Helsinki 2009. The colloquium was dedicated to Teivo Pentikäinen.

Keywords

Ruin probabilityinflationreal growthinvestmentcyclelarge deviation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 2 , November 2010 , pp. 889 - 915
Copyright
Copyright © International Actuarial Association 2010

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References

Asmussen, S. (2000) Ruin Probabilities. River Edge, NJ: World Scientific.CrossRefGoogle Scholar
Bahadur, R.R. and Zabell, S.L. (1979) Large deviations of the sample mean in general vector spaces. Ann. Probab. 7, 587–621.CrossRefGoogle Scholar
Brockwell, P.J. and Davis, R.A. (1991) Time Series: Theory and Methods (2nd ed.). New York: Springer Verlag.CrossRefGoogle Scholar
Collamore, J.F. (1998) First passage times of general sequences of random vectors: a large deviations approach. Stoch. Process. Appl. 78, 97–130.CrossRefGoogle Scholar
Collamore, J.F. (2009) Random recurrence equations and ruin in a Markov-dependent stochastic economic environment. Ann. Appl. Probab. 19, 1404–1458.CrossRefGoogle Scholar
Daykin, C.D., Pentikainen, T. and Pesonen, M. (1994) Practical Risk Theory for Actuaries. London: Chapman & Hall.Google Scholar
Dembo, A. and Zeitouni, O. (1998) Large Deviations Techniques and Applications (2nd ed.). Berlin: Springer-Verlag.CrossRefGoogle Scholar
Frolova, A., Kabanov, Y. and Pergamenchtchikov, S. (2002) In insurance business risky invest ments are dangerous. Finance and Stochastics 6, 227–235.CrossRefGoogle Scholar
Goldie, C.M. (1991) Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1, 126–166.CrossRefGoogle Scholar
Grandell, J. (1997) Mixed Poisson Processes. Chapman & Hall, London.CrossRefGoogle Scholar
Grey, D.R. (1994) Regular variation in the tail behaviour of solutions of random difference equations. Ann. Appl. Probab. 4, 169–183.CrossRefGoogle Scholar
Kalashnikov, V. and Norberg, R. (2002) Power tailed ruin probabilities in the presence of small claims and risky investments. Stoch. Proc. Appl. 98, 211–228.CrossRefGoogle Scholar
Martin-Löf, A. (1983) Entropy estimates for ruin probabilities. In Gut, A. and Holst, L. (Eds.), Probability and Mathematical Statistics, pp. 129–139. Uppsala University: Dept. of Mathematics.Google Scholar
Nyrhinen, H. (1998) Rough descriptions of ruin for a general class of surplus processes. Adv. Appl. Prob. 30, 1008–1026.CrossRefGoogle Scholar
Nyrhinen, H. (2001) Finite and infinite time ruin probabilities in a stochastic economic environment. Stoch. Proc. Appl. 92, 265–285.CrossRefGoogle Scholar
Nyrhinen, H. (2005) Power estimates for ruin probabilities. Adv. Appl. Prob. 37, 726–742.CrossRefGoogle Scholar
Panjer, H.H. (Ed.) (1998) Financial Economics. Schaumburg, IL: The Actuarial Foundation.Google Scholar
Paulsen, J. (1993) Risk theory in a stochastic economic environment. Stoch. Proc. Appl. 46, 327–361.CrossRefGoogle Scholar
Paulsen, J. (2002) On Cramer-like asymptotics for risk processes with stochastic return on in vestments. Ann. Appl. Probab. 12, 1247–1260.CrossRefGoogle Scholar
Paulsen, J. (2008) Ruin models with investment income. Probab. Surv. 5, 416–434.CrossRefGoogle Scholar
Pentikäinen, T., Bonsdorff, H., Pesonen, M., Rantala, J. and Ruohonen, M. (1989) Insurance Solvency and Financial Strength. Finnish Insurance Training and Publishing Company, Helsinki.Google Scholar
Pentikäinen, T. and Rantala, J. (1982) Solvency of Insurers and Equalization Reserves, Vol. I and II. The Insurance Publishing Company, Helsinki.Google Scholar
Rockafellar, R.T. (1970) Convex Analysis. Princeton: Princeton Univ. Press.CrossRefGoogle Scholar
Schnieper, R. (1983) Risk processes with stochastic discounting. Mitt. Verein. schweiz. Vers. Math. 83(2), 203–218.Google Scholar
The Conference of Insurance Supervisory Services of the Member States of the European Union (2002) Prudential supervision of insurance undertakings. Available on line at http://ec.europa.eu/internalmarket/insurance/docs/solvency/impactassess/annex-c02en.pdf.Google Scholar