Tang, Qihe (2005) The Finite Time Ruin Probability of the Compound Poisson Model with Constant Interest Force. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.

PDF
 Published Version
215kB 
Abstract
In this paper we establish a simple asymptotic formula with respect to large initial surplus for thefinite time ruin probability of the compound Poisson model with constant interest force and subexponential claims. The formula is consistent with known results for the ultimate ruin probability and, in particular, it is uniform for all
time horizons when the claim size distribution is regularly varying tailed.
Divisions:  Concordia University > Faculty of Arts and Science > Mathematics and Statistics 

Item Type:  Monograph (Technical Report) 
Authors:  Tang, Qihe 
Series Name:  Department of Mathematics & Statistics. Technical Report No. 2/05 
Corporate Authors:  Concordia University. Department of Mathematics & Statistics 
Institution:  Concordia University 
Date:  June 2005 
Keywords:  Asymptotics, finite time ruin probability, Poisson process, regular variation, subexponentiality, uniform convergence 
ID Code:  6666 
Deposited By:  DIANE MICHAUD 
Deposited On:  02 Jun 2010 16:34 
Last Modified:  08 Dec 2010 23:23 
References:  Asmussen, S. Subexponential asymptotics for stochastic processes: extremal behavior, stationary distributions and first passage probabilities. Ann. Appl. Probab. 8 (1998), no. 2, 354{374.
Asmussen, S.; Kalashnikov, V.; Konstantinides, D.; Klüppelberg, C.; Tsitsiashvili, G. A local limit theorem for random walk maxima with heavy tails. Statist. Probab. Lett. 56 (2002), no. 4, 399404. Athreya, K. B.; Ney, P. E. Branching processes. SpringerVerlag, New YorkHeidelberg, 1972. Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Cambridge University Press, Cambridge, 1987. Chistyakov, V. P. A theorem on sums of independent positive random variables and its applications to branching random processes. (Russian) Teor. Verojatnost. i Primenen 9 (1964), 710718; translation in Theor. Probability Appl. 9 (1964), 640648. Cline, D. B. H.; Samorodnitsky, G. Subexponentiality of the product of independent random variables. Stochastic Process. Appl. 49 (1994), no. 1, 7598. Embrechts, P.; Goldie, C. M.; Veraverbeke, N. Subexponentiality and in¯nite divisibility. Z. Wahrsch. Verw. Gebiete 49 (1979), no. 3, 335347. Embrechts, P.; Klüppelberg, C.; Mikosch, T. Modelling extremal events for insurance and finance. SpringerVerlag, Berlin, 1997. Embrechts, P.; Omey, E. A property of longtailed distributions. J. Appl. Probab. 21(1984), no. 1, 8087. Kalashnikov, V.; Konstantinides, D. Ruin under interest force and subexponential claims: a simple treatment. Insurance Math. Econom. 27 (2000), no. 1, 145149. Klüppelberg, C. Subexponential distributions and integrated tails. J. Appl. Probab. 25 (1988), no. 1, 132{141. Klüppelberg, C.; StadtmÄuller, U. Ruin probabilities in the presence of heavytails and interest rates. Scand. Actuar. J. (1998), no. 1, 4958. Konstantinides, D.; Tang, Q.; Tsitsiashvili, G. Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails. Insurance Math. Econom. 31 (2002), no. 3, 447460. Petrov, V. V. Limit theorems of probability theory. Sequences of independent random variables. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. Ross, S. M. Stochastic processes. John Wiley & Sons, Inc., New York, 1983. Sundt, B.; Teugels, J. L. Ruin estimates under interest force. Insurance Math. Econom. 16 (1995), no. 1, 722. Tang, Q. The ruin probability of a discrete time risk model under constant interest rate with heavy tails. Scand. Actuar. J. (2004), no. 3, 229240. Tang, Q. Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation. Scand. Actuar. J. (2005), no. 2, to appear. 
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
Downloads
Downloads per month over past year