Abstract
In examining the nature of the risk associated with a portfolio of business, it is often of interest to assess how the portfolio may be expected to perform over an extended period of time. One approach involves the use of ruin theory (Panjer and Willmot, 1992). Ruin theory is concerned with the excess of the income (with respect to a portfolio of business) over the outgo, or claims paid. This quantity, referred to as insurer’s surplus, varies in time. Specifically, ruin is said to occur if the insurer’s surplus reaches a specified lower bound, e.g. minus the initial capital. One measure of risk is the probability of such an event, clearly reflecting the volatility inherent in the business. In addition, it can serve as a useful tool in long range planning for the use of insurer’s funds.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Asmussen, S. (2000). Ruin Probabilities, World Scientific, Singapore.
Burnecki, K. (2000). Self-similar processes as weak limits of a risk reserve
process, Probab. Math. Statist. 20(2): 261-272.
Burnecki, K., Mi´sta, P., and Weron, A. (2005). Ruin Probabilities in Finite
and Infinite Time, in P. Cizek, W. H¨ardle, and R. Weron (eds.) Statistical
Tools for Finance and Insurance, Springer, Berlin, 341-379.
Burnecki, K., Mi´sta, P., andWeron, A. (2005). What is the best approximation
of ruin probability in infinite time?, Appl. Math. (Warsaw) 32(2): 155-
176.
Degen, M., Embrechts, P., and Lambrigger, D.D. (2007). The quantitative
modeling of operational risk: between g-and-h and EVT, Astin Bulletin
37(2): 265-291.
Embrechts, P., Kaufmann, R., and Samorodnitsky, G. (2004). Ruin Theory
Revisited: Stochastic Models for Operational Risk, in C. Bernadell et al
(eds.) Risk Management for Central Bank Foreign Reserves, European
Central Bank, Frankfurt a.M., 243-261.
Furrer, H., Michna, Z., and Weron, A. (1997). Stable L´evy motion approximation
in collective risk theory, Insurance Math. Econom. 20: 97–114.
Grandell, J. (1991). Aspects of Risk Theory, Springer, New York.
Iglehart, D. L. (1969). Diffusion approximations in collective risk theory, Journal
of Applied Probability 6: 285–292.
Kaishev, V.K., Dimitrova, D.S. and Ignatov, Z.G. (2008). Operational risk and
insurance: a ruin-probabilistic reserving approach, Journal of Operational
Risk 3(3): 39–60.
Nolan, J.P. (2010). Stable Distributions - Models for Heavy Tailed
Data, Birkhauser, Boston, In progress, Chapter 1 online at
academic2.american.edu/∼jpnolan.
Panjer, H.H. and Willmot, G.E. (1992). Insurance Risk Models, Society of
Actuaries, Schaumburg.
Segerdahl, C.-O. (1955). When does ruin occur in the collective theory of risk?
Skand. Aktuar. Tidskr 38: 22–36.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Burnecki, K., Teuerle, M. (2011). Ruin probability in finite time. In: Cizek, P., Härdle, W., Weron, R. (eds) Statistical Tools for Finance and Insurance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18062-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-18062-0_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18061-3
Online ISBN: 978-3-642-18062-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)