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Recursive evaluation of aggregate claims distributions

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  • Sundt, Bjorn

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  • Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    • Handle: RePEc:eee:insuma:v:30:y:2002:i:3:p:297-322
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    1. Willmot, Gord, 1986. "Mixed Compound Poisson Distributions," ASTIN Bulletin, Cambridge University Press, vol. 16(S1), pages 59-79, April.
    2. Gerber, Hans U., 1982. "On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 13-18, January.
    3. H. Panjer, Harry & Shaun Wang,, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 227-258, November.
    4. Hipp, Christian, 1986. "Improved Approximations for the Aggregate Claims Distribution in the Individual Model," ASTIN Bulletin, Cambridge University Press, vol. 16(2), pages 89-100, November.
    5. Sundt, Bjorn, 2000. "The multivariate De Pril transform," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 123-136, August.
    6. Jewell, W. S. & Milidiu, R. L., 1986. "Strategies for computation of compound distributions with two-sided severities," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 119-127, April.
    7. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
    8. Hesselager, Ole, 1994. "A Recursive Procedure for Calculation of some Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 19-32, May.
    9. Waldmann, Karl-Heinz, 1996. "Modified Recursions for a Class of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 213-224, November.
    10. Ambagaspitiya, Rohana S., 1998. "Compound bivariate Lagrangian Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 21-31, October.
    11. De Pril, Nelson, 1985. "Recursions for Convolutions of Arithmetic Distributions," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 135-139, November.
    12. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
    13. Wang, Shaun & Sobrero, Monica, 1994. "Further Results on Hesselager's Recursive Procedure for Calculation of some Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 161-166, November.
    14. Walhin, J.F. & Paris, J., 2001. "The Mixed Bivariate Hofmann Distribution," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 123-138, May.
    15. Chan, Beda, 1982. "Recursive formulas for discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 1(4), pages 241-243, October.
    16. Ambagaspitiya, Rohana S., 1999. "On the distributions of two classes of correlated aggregate claims," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 301-308, May.
    17. Willmot, G. E. & Panjer, H. H., 1987. "Difference equation approaches in evaluation of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 6(1), pages 43-56, January.
    18. Sundt, Bjørn, 2000. "On Multivariate Vernic Recursions," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 111-122, May.
    19. Waldmann, Karl-Heinz, 1994. "On the Exact Calculation of the Aggregate Claims Distribution in the Individual Life Model," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 89-96, May.
    20. Goovaerts, M. J. & Kaas, R., 1991. "Evaluating Compound Generalized Poisson Distributions Recursively," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 193-198, November.
    21. De Pril, Nelson, 1986. "Improved recursions for some compound poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 129-132, April.
    22. Sundt, Bjorn, 2000. "On error bounds for approximations to multivariate distributions," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 137-144, August.
    23. Sundt, Bjørn, 1999. "On Multivariate Panjer Recursions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 29-45, May.
    24. Walhin, J.F. & Paris, J., 2000. "Recursive Formulae for Some Bivariate Counting Distributions Obtained by the Trivariate Reduction Method," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 141-155, May.
    25. Wang, Shaun & Panjer, Harry, 1994. "Proportional convergence and tail-cutting techniques in evaluating aggregate claim distributions," Insurance: Mathematics and Economics, Elsevier, vol. 14(2), pages 129-138, May.
    26. Sundt, Bjørn & Jewell, William S., 1981. "Further Results on Recursive Evaluation of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 27-39, June.
    27. De Pril, Nelson, 1986. "On the Exact Computation of the Aggregate Claims Distribution in the Individual Life Model," ASTIN Bulletin, Cambridge University Press, vol. 16(2), pages 109-112, November.
    28. Sundt, Bjørn, 1995. "On Some Properties of de Pril Transforms of Counting Distributions," ASTIN Bulletin, Cambridge University Press, vol. 25(1), pages 19-31, May.
    29. Wang, Shaun & Panjer, Harry, 1993. "Critical starting points for stable evaluation of mixed Poisson probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 287-297, December.
    30. Dhaene, Jan & Sundt, Bjørn & De Pril, Nelson, 1996. "Some Moment Relations for the Hipp approximation," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 117-121, May.
    31. Panjer, Harry H. & Willmot, Gordon E., 1986. "Computational aspects of recursive evaluation of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 113-116, January.
    32. De Pril, Nelson, 1989. "The Aggregate Claims Distribution in the Individual Model with Arbitrary Positive Claims," ASTIN Bulletin, Cambridge University Press, vol. 19(1), pages 9-24, April.
    33. Panjer, H. H. & Lutek, B. W., 1983. "Practical aspects of stop-loss calculations," Insurance: Mathematics and Economics, Elsevier, vol. 2(3), pages 159-177, July.
    34. Vernic, Raluca, 1999. "Recursive Evaluation of Some Bivariate Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 315-325, November.
    35. Sundt, Bjorn, 1991. "On asymptotic rates on line in excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 61-67, March.
    36. Dhaene, Jan & Pril, Nelson De, 1994. "On a class of approximative computation methods in the individual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 14(2), pages 181-196, May.
    37. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
    38. Hesselager, Ole, 1996. "Recursions for certain bivariate counting distributions and their compound distributions," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 35-52, May.
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    Cited by:

    1. Mariana Arozo B. de Melo & Cristiano A. C. Fernandes & Eduardo F. L. de Melo, 2018. "Forecasting aggregate claims using score‐driven time series models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 354-374, August.
    2. Chuancun Yin & Jing Yao & Yang Yang, 2024. "Hessian and increasing-Hessian orderings of multivariate skew-elliptical random vectors with applications in actuarial science," Statistical Papers, Springer, vol. 65(7), pages 4715-4744, September.
    3. Eisele, Karl-Theodor, 2006. "Recursions for compound phase distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 149-156, February.
    4. Sangüesa, C., 2008. "Error bounds in approximations of random sums using gamma-type operators," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 484-491, April.
    5. Chadjiconstantinidis, Stathis & Pitselis, Georgios, 2009. "Further improved recursions for a class of compound Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 278-286, April.
    6. Sanguesa, C., 2006. "Approximations of ruin probabilities in mixed Poisson models with lattice claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 69-80, August.
    7. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2020. "A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums," Risks, MDPI, vol. 8(1), pages 1-19, February.
    8. Mehdi Amiri & Narayanaswamy Balakrishnan & Abbas Eftekharian, 2022. "Hessian orderings of multivariate normal variance-mean mixture distributions and their applications in evaluating dependent multivariate risk portfolios," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 679-707, September.

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