Computation of compound distributions i: Aliasing errors and exponential tilting

ASTIN Bulletin

Volumn 29, Issue 2, 1999, Pages 197-214

  Grübel, Rudolf ^a   Hermesmeier, Renate ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

aliasing; change of measure; Fourier transformation; random sums; ruin probabilities; Total claim size distribution

Indexed keywords

EID: 85011437009     PISSN: 05150361     EISSN: 17831350     Source Type: Journal    
DOI: 10.2143/AST.29.2.504611     Document Type: Article

References (19)

1. Asmussen, S. (1987). Applied Probability and Queues. Wiley, Chichester.
2. Asmussen, S. and Binswanger, K. (1997). Simulation of ruin probabilities for subexponential claims. ASTIN Bull. 27, 27–297.
3. Beard, R.E., Pentikäinen, T. and Personen, E. (1984). Risk Theory: The Stochastic Basis of Insurance. (3rd ed.) Chapman and Hall, London.
4. Buchwalder, M., Chevalier, E. and Kluppelberg, C. (1993). Approximation methods for the total claimsize distribution-an algorithmic and graphical presentation. Mitteilungen der Schweiz. Vereinigung der Versicherungsmathematiker, Heft 2/1993.
5. Bühlmann, H. (1984). Numerical evaluation of the compound Poisson distribution: recursion or fast Fourier transform? Scand. Actuarial J. 2, 2–116.
6. Chover, J., Ney, P. and Wainger, S. (1973). Functions of probability measures. J. Analyse Math. 26, 26–255.
7. Embrechts, P., Goldie, C.M. and Veraverbeke, N. (1979). Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitstheorie verw. Gebiete. 49, 49–335.
8. Embrechts, P., Grübel, R. and Pitts, S.M. (1993). Some applications of the fast Fourier transform algorithm in insurance mathematics. Statistica Neerlandica. 47, 47–59.
9. Embrechts, P., Klüppelberg, C. and Mikosch, Th. (1997). Modelling Extremal Events. Springer, Berlin.
10. Embrechts, P. and Veraverbeke, N. (1982). Estimates of the probability of ruin with special emphasis on the possibility of large claims. Insurance: Mathematics and Economics. 1, 1–55.
11. Grandell, J. (1991). Aspects of Risk Theory. Springer, New York.
12. Grübel, R. (1991). Algorithm AS 265: G/G/1 via Fast Fourier Transform. Applied Statistics (J. R. Stat. Soc. C). 40, 40–355.
13. Grübel, R. and Hermesmeier, R. (1999). Computation of compound distributions II: discretization errors and Richardson extrapolation. In preparation.
14. Hermesmeier, R. (1997). Transformationsmethoden und Diskretisierungsefjekte bei stochastischen Modellen in der Versicherungsmathematik. Doctoral thesis, University of Hannover.
15. Hipp, C. and Michel, R. (1990). Risikotheorie: Stochastische Modelle und Statistische Methoden, Verlag Versicherungswirtschaft e.V., Karlsruhe.
16. Johnson, N.L., Kotz, S. and Kemp, A.W. (1992). Univariate Discrete Distributions, 2nd edition. Wiley, New York.
17. Panjer, H.H. (1981). Resursive evaluation of a family of compound distributions. ASTIN Bulletin. 12, 12–22.
18. Pitts, S.M. (1994). Nonparametric estimation of compound distributions with applications in insurance. Ann. Inst. Stat. Math. 46, 46–537.
19. Schröter, K.J. (1995). Verfahren zur Approximation der Gesamtschadenverteilung: System-atisierung, Techniken und Vergleiche. Verlag Versicherungswirtschaft e.V., Karlsruhe.