The finite-time ruin probability of the compound Poisson model with constant interest force

The finite-time ruin probability of the compound Poisson model with constant interest force

Qihe Tang

Source: J. Appl. Probab. Volume 42, Number 3 (2005), 608-619.

Abstract

In this paper, we establish a simple asymptotic formula for the finite-time ruin probability of the compound Poisson model with constant interest force and subexponential claims in the case that the initial surplus is large. The formula is consistent with known results for the ultimate ruin probability and, in particular, is uniform for all time horizons when the claim size distribution is regularly varying tailed.

Primary Subjects: 91B30

Secondary Subjects: 60G70, 62P05

Keywords: Asymptotics; finite-time ruin probability; Poisson process; regular variation; subexponentiality; uniform asymptotics; uniform convergence

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1127322015
Digital Object Identifier: doi:10.1239/jap/1127322015
Mathematical Reviews number (MathSciNet): MR2157508
Zentralblatt MATH identifier: 05001861

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References

Asmussen, S. (1998). Subexponential asymptotics for stochastic processes: extremal behavior, stationary distributions and first passage probabilities. Ann. Appl. Prob. 8, 354--374.

Mathematical Reviews (MathSciNet): MR1624933

Digital Object Identifier: doi:10.1214/aoap/1028903531

Project Euclid: euclid.aoap/1028903531

Asmussen, S. et al. (2002). A local limit theorem for random walk maxima with heavy tails. Statist. Prob. Lett. 56, 399--404.

Mathematical Reviews (MathSciNet): MR1898718

Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, New York.

Mathematical Reviews (MathSciNet): MR373040

Zentralblatt MATH: 0259.60002

Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular Variation. Cambridge University Press.

Mathematical Reviews (MathSciNet): MR898871

Zentralblatt MATH: 0617.26001

Chistyakov, V. P. (1964). A theorem on sums of independent positive random variables and its applications to branching random processes. Teor. Veroyat. Primen. 9, 710--718 (in Russian). English translation: Theory Prob. Appl. 9, 640--648.

Mathematical Reviews (MathSciNet): MR170394

Cline, D. B. H. and Samorodnitsky, G. (1994). Subexponentiality of the product of independent random variables. Stoch. Process. Appl. 49, 75--98.

Mathematical Reviews (MathSciNet): MR1258283

Digital Object Identifier: doi:10.1016/0304-4149(94)90113-9

Embrechts, P. and Omey, E. (1984). A property of longtailed distributions. J. Appl. Prob. 21, 80--87.

Mathematical Reviews (MathSciNet): MR732673

Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979). Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth. 49, 335--347.

Mathematical Reviews (MathSciNet): MR547833

Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.

Mathematical Reviews (MathSciNet): MR1458613

Zentralblatt MATH: 0873.62116

Kalashnikov, V. and Konstantinides, D. (2000). Ruin under interest force and subexponential claims: a simple treatment. Insurance Math. Econom. 27, 145--149.

Mathematical Reviews (MathSciNet): MR1796976

Klüppelberg, C. (1988). Subexponential distributions and integrated tails. J. Appl. Prob. 25, 132--141.

Mathematical Reviews (MathSciNet): MR929511

Klüppelberg, C. and Stadtmüller, U. (1998). Ruin probabilities in the presence of heavy-tails and interest rates. Scand. Actuarial J. 1998, 49--58.

Mathematical Reviews (MathSciNet): MR1626664

Konstantinides, D., Tang, Q. and Tsitsiashvili, G. (2002). Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails. Insurance Math. Econom. 31, 447--460.

Mathematical Reviews (MathSciNet): MR1945543

Nagaev, S. V. (1979). Large deviations of sums of independent random variables. Ann. Prob. 7, 745--789.

Mathematical Reviews (MathSciNet): MR542129

JSTOR: links.jstor.org

Petrov, V. V. (1995). Limit Theorems of Probability Theory. Sequences of Independent Random Variables. Oxford University Press.

Mathematical Reviews (MathSciNet): MR1353441

Zentralblatt MATH: 0826.60001

Ross, S. M. (1983). Stochastic Processes. John Wiley, New York.

Mathematical Reviews (MathSciNet): MR683455

Zentralblatt MATH: 0555.60002

Sundt, B. and Teugels, J. L. (1995). Ruin estimates under interest force. Insurance Math. Econom. 16, 7--22.

Mathematical Reviews (MathSciNet): MR1342906

Tang, Q. (2004). The ruin probability of a discrete time risk model under constant interest rate with heavy tails. Scand. Actuarial J. 2004, 229--240.

Mathematical Reviews (MathSciNet): MR2064607

Digital Object Identifier: doi:10.1080/03461230310017531

Tang, Q. (2005). Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation. Scand. Actuarial J. 2005, 1--5.

Mathematical Reviews (MathSciNet): MR2118521

Tang, Q. and Tsitsiashvili, G. (2003). Randomly weighted sums of subexponential random variables with application to ruin theory. Extremes 6, 171--188.

Mathematical Reviews (MathSciNet): MR2081850

Digital Object Identifier: doi:10.1023/B:EXTR.0000031178.19509.57

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