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, 399-404.

Athreya, K. B.; Ney, P. E. Branching processes. Springer-Verlag, New York-Heidelberg,
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), 710-718; translation in Theor. Probability Appl. 9 (1964), 640-648.

Cline, D. B. H.; Samorodnitsky, G. Subexponentiality of the product of independent random variables. Stochastic Process. Appl. 49 (1994), no. 1, 75-98.

Embrechts, P.; Goldie, C. M.; Veraverbeke, N. Subexponentiality and in¯nite divisibility. Z. Wahrsch. Verw. Gebiete 49 (1979), no. 3, 335-347.

Embrechts, P.; Klüppelberg, C.; Mikosch, T. Modelling extremal events for insurance and finance. Springer-Verlag, Berlin, 1997.

Embrechts, P.; Omey, E. A property of longtailed distributions. J. Appl. Probab. 21(1984), no. 1, 80-87.

Kalashnikov, V.; Konstantinides, D. Ruin under interest force and subexponential claims: a simple treatment. Insurance Math. Econom. 27 (2000), no. 1, 145-149.

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 heavy-tails and interest rates. Scand. Actuar. J. (1998), no. 1, 49-58.

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, 447-460.

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, 7-22.

Tang, Q. The ruin probability of a discrete time risk model under constant interest rate with heavy tails. Scand. Actuar. J. (2004), no. 3, 229-240.

Tang, Q. Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation. Scand. Actuar. J. (2005), no. 2, to appear.