The Tail Probability of Discounted Sums of Pareto-Like Losses in Insurance


The Tail Probability of Discounted Sums of Pareto-Like Losses in Insurance

Goovaerts, Marc J. and Kaas, Rob and Laeven, Roger J.A. and Tang, Qihe and Vernic, Raluca (2005) The Tail Probability of Discounted Sums of Pareto-Like Losses in Insurance. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.

PDF - Published Version


In an insurance context, the discounted sum of losses within afinite or ifinite time period can be described as a randomly weighted sum of a sequence of independent random variables. These independent random variables represent the amounts of losses in successive development years, while the weights represent the stochastic discount factors. In this paper, we investigate the problem of approximating the
tail probability of this weighted sum in the case when the losses have Pareto-like distributions and the discount factors are mutually dependent. We also give some simulation results.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Monograph (Technical Report)
Authors:Goovaerts, Marc J. and Kaas, Rob and Laeven, Roger J.A. and Tang, Qihe and Vernic, Raluca
Series Name:Department of Mathematics & Statistics. Technical Report No. 3/05
Corporate Authors:Concordia University. Department of Mathematics & Statistics
Institution:Concordia University
Date:August 2005
Keywords:Asymptotics; (Log)elliptical distribution; (Log)normal variance-mean mixed distribution; Pareto-like distribution; Tail probability
ID Code:6668
Deposited On:02 Jun 2010 12:36
Last Modified:08 Dec 2010 18:22
Barndorff-Nielsen, O.E. (1997)."Normal inverse Gaussian distributions and stochastic volatility modelling," Scandinavian Journal of Statistics 24, no. 1, 1-13.

Beirlant, J., J.L. Teugels & P. Vynckier (1996). Practical analysis of extreme values, Leuven: Leuven University Press.

Bingham, N.H., C.M. Goldie & J.L. Teugels (1987). Regular variation, Cambridge: Cambridge University Press.

Bingham, N.H., R. Kiesel & R. Schmidt (2003). "A semi-parametric approach to risk management," Quantitative Finance 3, no. 6, 426-441.

Breiman, L. (1965). "On some limit theorems similar to the arc-sin law," Theory of Probability and its Applications 10, no. 2, 323-331.

Cline, D.B.H. & G. Samorodnits (1994). "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications 49, no. 1, 75-98.

Davis, R.A. & S.I. Resnick (1996). "Limit theory for bilinear processes with heavy-tailed noise," The Annals of Applied Probability 6, no. 4, 1191-1210.

Eberlein, E. & U. Keller (1995). "Hyperbolic distributions in finance," Bernoulli 1, no. 3, 281-299.

Fang, K.T., S. Kotz & K.W. Ng (1990). Symmetric multivariate and related distributions, London: Chapman and Hall.

Gupta, A.K. & T. Varga (1993). Elliptically contoured models in statistics, Dordrecht: Kluwer Academic Publishers.

Norberg, R. (1999). "Ruin problems with assets and liabilities of diffusion type,"Stochastic Processes and their Applications 81, no. 2, 255-269.

Nyrhinen, H. (1999). "On the ruin probabilities in a general economic environment,"Stochastic Processes and their Applications 83, no. 2, 319-330.

Owen, J. & R. Rabinovitch (1983). "On the class of elliptical distributions and their applications to the theory of portfolio choice," Journal of Finance 38, no. 3, 745-752.

Resnick, S.I. & E. Willekens (1991). "Moving averages with random coefficients and random coefficient autoregressive models," Communications in Statistics - Stochastic Models 7, no. 4, 511-525.

Tang, Q. & G. Tsitsiashvili (2003). "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications 108, no. 2, 299-325.

Tang, Q. & G. Tsitsiashvili (2004). "Finite and ifinite time ruin probabilities in the presence of stochastic return on investments," Advances in Applied Probability 36, no. 4, 1278-1299.

Vorkink, K. (2003). "Return distributions and improved tests of asset pricing models,"Review of Financial Studies 16, no. 3, 845-874.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Document Downloads

More statistics for this item...

Concordia University - Footer