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The discrete-time risk model with correlated classes of business. (English) Zbl 1103.91358
Summary: The discrete-time risk model with correlated classes of business is examined. Two different relations of dependence are considered. The impact of the dependence relation on the finite-time ruin probabilities and on the adjustment coefficient is also studied. Numerical examples are presented.

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI
[1] Ambagaspitiya, R.S., On the distribution of a sum of correlated aggregated claims, Insurance: mathematics and economics, 23, 15-19, (1998) · Zbl 0916.62072
[2] Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J., 1997. Actuarial Mathematics. Society of Actuaries, Schaumburg, IL.
[3] Bühlmann, H., 1970. Mathematical Methods in Risk Theory. Springer, New York.
[4] Bühlmann, H., 1984. Numerical evaluation of the compound Poisson distribution: recurson or fast Fourier transform? Scandinavian Actuarial Journal, pp. 116-126.
[5] Cummins, J.D., Wiltbank, L.J., 1983. Estimating the total claims distribution using multivariate frequency and severity distributions. Journal of Risk and Insurance, pp. 377-403.
[6] De Vylder, F.; Goovaerts, M.J., Recursive calculation of finite-time ruin probabilities, Insurance: mathematics and economics, 7, 1-8, (1988) · Zbl 0629.62101
[7] Dickson, D.C.M.; Waters, H., Recursive calculation of survival probabilities, ASTIN bulletin, 21, 199-221, (1991)
[8] Gerber, H.U., 1979. An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation, University of Pennsylvania, Philadelphia. · Zbl 0431.62066
[9] Goovaerts, M.J., Kaas, R., van Heerwarden, A.E., Bauwelinckx, T., 1990. Effective Actuarial Methods. North-Holland, Amsterdam.
[10] Heckman, P.E., Meyers, G.G., 1983. The calculation of aggregate loss distributions from claim severity and claim count distributions. Proceedings of the Casualty Actuarial Society LXX, pp. 22-61.
[11] Hesselager, O., Recursions for certain bivariate counting distributions and their compound distributions, ASTIN bulletin, 26, 35-52, (1996)
[12] Klugman, S.A., Panjer, H.H., Willmot, G.E., 1998. Loss Models: From Data to Decisions. Wiley, New York. · Zbl 0905.62104
[13] Kocherlakota, S., Kocherlakota, K., 1992. Bivariate Discrete Distributions. Marcel Dekker, New York. · Zbl 0794.62002
[14] Marshall, A.W.; Olkin, I., A multivariate exponential distribution, Journal of the American statistical association, 62, 30-44, (1967) · Zbl 0147.38106
[15] Marshall, A.W.; Olkin, I., Families of multivariate distributions, Journal of the American statistical association, 83, 834-841, (1988) · Zbl 0683.62029
[16] Panjer, H.H., Willmot, G.E., 1992. Insurance Risk Models. Society of Actuaries, Schaunmburg, IL.
[17] Robertson, J., 1992. The computation of aggregate loss distributions. Proceedings of the Casualty Actuarial Society LXXIX, pp. 57-133.
[18] Rolski, T., Schmidli, H., Schmidt, V., Teugels, J., 1999. Stochastic Processes for Insurance and Finance. Wiley, New York. · Zbl 0940.60005
[19] Wang, S., 1998. Aggregation of correlated risk portfolios: models and algorithms. Proceedings of the Casualty Actuarial Society, 848-939.
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