Applications of Mogulskii, and Kurtz-Feng Large Deviation Results to Risk Reserve Processes with Aggregate Claims

Show more

References

[1] A. A. Mogulskii, “Large Deviations for Processes with Independent Increments,” Annals of Probability, Vol. 21, No. 1, 1993, pp. 202-215. doi:10.1214/aop/1176989401

[2] J. Lynch and J. Sethuraman, “Large Deviations for Processes with Independent Increments,” Annals of Probability, Vol. 15, No. 2, 1987, pp. 610-627.
doi:10.1214/aop/1176992161

[3] A. de Acosta, “Large Deviations for Vector-Valued Lévy Processes,” Stochastic Processes and Their Applications, Vol. 51, No. 1, 1994, pp. 75-115.
doi:10.1016/0304-4149(94)90020-5

[4] A. de Acosta, “Exponential Tightness and Projective Systems in Large Deviation Theory,” In: D. Pollard, E. Togersen and G. Yang, Eds., Festschrift for Lucien Le Cam, Springer, New York, 1997, pp. 143-156.

[5] Z. H. Li and E. A. Pechersky, “On Large Deviations in Queuing Systems,” Resenha, Vol. 4, No. 2, 1999, pp. 163-182.

[6] R. L. Dobrushin and E. A. Pechersky, “Large Deviations for Tandem Queueing Systems,” Journal of Applied Ma- thematics and Stochastic Analysis, Vol. 7, No. 3, 1994, pp. 301-330. doi:10.1155/S1048953394000274

[7] A. Ganesh, C. Macci and G. L.Torrisi, “A Class of Risk Processes with Reserve-Dependent Premium Rate: Sample Path Large Deviations and Importance Sampling,” Queueing Systems, Vol. 55, No. 2, 2007, pp. 83-94.
doi:10.1007/s11134-006-9000-y

[8] A. Ganesh, C. Macci and G. L. Torrisi, “Sample Path Large Deviations Principles for Poisson Shot Noise Proc- esses, and Applications,” Electronic Journal of Probabil- ity, Vol. 10, No. 32, 2005, pp. 1026-1043.

[9] J. Feng and T. G. Kurtz, “Large Deviations for Stochastic Processes,” Vol. 131, Mathematical Surveys and Monographs, American Mathematical Society, Providence, 2006.

[10] S. Asmussen, “Ruin Probabilities,” Vol. 2, Advanced Series on Statistical Science & Applied Probability, World Scientific Publishing Co. Inc., River Edge, 2000.

[11] S. Asmussen and C. Klüppelberg, “Large Deviations Results for Subexponential Tails, with Applications to Insurance Risk,” Stochastic Processes and their Applications, Vol. 64, No. 1, 1996, pp. 103-125.
doi:10.1016/S0304-4149(96)00087-7

[12] C. Klüppelberg and T. Mikosch, “Large Deviations of Heavy-Tailed Random Sums with Applications in Insurance and Finance,” Journal of Applied Probability, Vol. 34, No. 2, 1997, pp. 293-308. doi:10.2307/3215371

[13] G. R. Shorack and J. A. Wellner, “Empirical processes with applications to statistics of Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics,” John Wiley & Sons Inc., New York, 1986.

[14] P. Embrechts, C. Klüppelberg and T. Mikosch, “Modelling Extremal Events,” Vol. 33, Applications of Mathematics, Springer-Verlag, Berlin, 1997.