The probability of ruin in finite time

Lithuanian Mathematical Journal

Volumn 39, Issue 3, 1999, Pages 240-244

  Baltrunas A ^a  

^a VILNIUS UNIVERSITY   (Lithuania)

Author keywords

Integrated tails; Ruin probability; Sparre Andersen model; Subexponential distributions

Indexed keywords

EID: 24244471909     PISSN: 03631672     EISSN: 15738825     Source Type: Journal    
DOI: 10.1007/BF02465844     Document Type: Article

References (14)

1. E. Sparre Andersen, On the collective theory of risk in case of contagion between claims, in: Transactions XV International Congress of Actuaries, II, New York (1957), pp. 219-229.
2. S. Asmussen, Approximations for the probability of ruin within finite time, Scand. Act. J., 31-57 (1984).
3. S. Asmussen and C. Klüppelberg, Large deviations results for subexponential distributions, with applications to insurance risk, Stoc. Proc. Appl., 64, 103-125 (1996).
4. S. Asmussen and J. L. Teugels, Convergence rates for M|G|1 queues and ruin problems with heavy tails, J. Appl. Prob., 33, 1181-1190(1996).
5. B. von Bahr, Asymptotic ruin probability when exponential moments do not exist, Scand. Actuarial J., 1, 6-10 (1975).
6. O. Barndorff-Nielsen and H. Schmidli, A saddlepoint approximation for finite time ruin probabilities, Scand. Act. J., 169-186 (1995).
7. A. A. Borovkov, Stochastic Processes in Queueing Theory, Springer, Berlin (1976).
8. V. P. Chistyakov, A theorem on sums of independent positive random variables and its application to branching random processes, Theor. Probab. Appl., 9, 640-648 (1964).
9. J. W. Cohen, The Single Server Queue. 2nd edn., North-Holland, Amsterdam (1982).
10. P. Embrechts and N. Veraverbeke, Estimates for the probability of ruin with special emphasis on the possibility of large claims, Insurance: Math. Econ., 1, 55-72 (1982).
11. C. M. Goldie and C. Klüppelberg, Subexponential distributions, in: A Practical Guide to Heavy Tails: Statistical Techniques for Analysing Heavy Tailed Distributions, R. Adler, R. Feldman, and M. S. Taqqu (Eds.), Birkhäuser, Basel (1998), pp. 435-459.
12. J. Grandell, Finite time ruin probabilities and martingales, Informatica, 2(1), 3-32 (1991).
13. O. Thorin and N. Wikstad, Calculation of ruin probabilities when the claim distribution is lognormal, ASTIN Bull., 9, 231-246 (1977).
14. H. Thorisson, The queue G1|G|1: Finite moments of the cycle variables and uniform rates of convergence, Stock. Proc. Appl., 19, 85-99 (1985).