IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v30y2002i3p297-322.html

Recursive evaluation of aggregate claims distributions

Author

Listed:
  • Sundt, Bjorn

Abstract

No abstract is available for this item.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(02)00123-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. repec:cup:astinb:v:16:y:1986:i:s1:p:s59-s79_01 is not listed on IDEAS
    2. repec:cup:astinb:v:24:y:1994:i:01:p:89-96_00 is not listed on IDEAS
    3. 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.
    4. repec:cup:astinb:v:21:y:1991:i:02:p:193-198_00 is not listed on IDEAS
    5. Ambagaspitiya, Rohana S., 1998. "Compound bivariate Lagrangian Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 21-31, October.
    6. repec:cup:astinb:v:23:y:1993:i:02:p:227-258_01 is not listed on IDEAS
    7. 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.
    8. De Pril, Nelson, 1986. "Improved recursions for some compound poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 129-132, April.
    9. repec:cup:astinb:v:19:y:1989:i:01:p:9-24_00 is not listed on IDEAS
    10. Walhin, J.F. & Paris, J., 2000. "The Effect of Excess-of-Loss Reinsurance with Reinstatements of the Cedent's Portfolio," Papers 3, Catholique de Louvain - Institut de statistique.
    11. repec:cup:astinb:v:15:y:1985:i:02:p:135-139_00 is not listed on IDEAS
    12. repec:cup:astinb:v:16:y:1986:i:02:p:89-100_00 is not listed on IDEAS
    13. Sundt, Bjorn, 2000. "On error bounds for approximations to multivariate distributions," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 137-144, August.
    14. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
    15. repec:cup:astinb:v:24:y:1994:i:02:p:161-166_00 is not listed on IDEAS
    16. Walhin, J.F. & Paris, J., 2001. "The Mixed Bivariate Hofmann Distribution," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 123-138, May.
    17. Sundt, Bjorn, 2000. "The multivariate De Pril transform," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 123-136, August.
    18. 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.
    19. 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.
    20. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
    21. Vernic, Raluca, 1999. "Recursive Evaluation of Some Bivariate Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 315-325, November.
    22. Chan, Beda, 1982. "Recursive formulas for discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 1(4), pages 241-243, October.
    23. 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.
    24. 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.
    25. repec:cup:astinb:v:24:y:1994:i:01:p:19-32_00 is not listed on IDEAS
    26. Sundt, Bjørn, 1999. "On Multivariate Panjer Recursions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 29-45, May.
    27. 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.
    28. 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.
    29. 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.
    30. repec:cup:astinb:v:26:y:1996:i:02:p:213-224_00 is not listed on IDEAS
    31. 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.
    32. repec:cup:astinb:v:12:y:1981:i:01:p:22-26_00 is not listed on IDEAS
    33. repec:cup:astinb:v:26:y:1996:i:01:p:35-52_00 is not listed on IDEAS
    34. repec:cup:astinb:v:12:y:1981:i:01:p:27-39_00 is not listed on IDEAS
    35. repec:cup:astinb:v:16:y:1986:i:02:p:109-112_00 is not listed on IDEAS
    36. repec:cup:astinb:v:25:y:1995:i:01:p:19-31_00 is not listed on IDEAS
    37. Sundt, Bjørn, 2000. "On Multivariate Vernic Recursions," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 111-122, May.
    38. 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.
    39. repec:cup:astinb:v:26:y:1996:i:01:p:117-121_00 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gathy, Maude & Lefèvre, Claude, 2010. "On the Lagrangian Katz family of distributions as a claim frequency model," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 76-83, August.
    2. Paul Embrechts & Marco Frei, 2009. "Panjer recursion versus FFT for compound distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 497-508, July.
    3. Sundt, Bjorn, 2000. "The multivariate De Pril transform," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 123-136, August.
    4. Eisele, Karl-Theodor, 2008. "Recursions for multivariate compound phase variables," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 65-72, February.
    5. Sundt, Bjorn, 2000. "On error bounds for approximations to multivariate distributions," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 137-144, August.
    6. Anastasiadis, Simon & Chukova, Stefanka, 2012. "Multivariate insurance models: An overview," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 222-227.
    7. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2017. "Polynomial Approximations for Bivariate Aggregate Claims Amount Probability Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 151-174, March.
    8. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
    9. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    10. Yuki Itoh, 2009. "Recovery Process Model for Two Companies," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(4), pages 287-331, December.
    11. Pablo Azcue & Nora Muler & Zbigniew Palmowski, 2016. "Optimal dividend payments for a two-dimensional insurance risk process," Papers 1603.07019, arXiv.org, revised Apr 2018.
    12. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    13. Irmina Czarna & Zbigniew Palmowski, 2009. "De Finetti's dividend problem and impulse control for a two-dimensional insurance risk process," Papers 0906.2100, arXiv.org, revised Feb 2011.
    14. Bermúdez i Morata, Lluís, 2009. "A priori ratemaking using bivariate Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 135-141, February.
    15. Lluis Bermúdez i Morata, 2008. "A priori ratemaking using bivariate poisson regression models," Working Papers XREAP2008-09, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008.
    16. Vilar, Jose L., 2000. "Arithmetization of distributions and linear goal programming," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 113-122, August.
    17. Zhang, Huiming & Liu, Yunxiao & Li, Bo, 2014. "Notes on discrete compound Poisson model with applications to risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 325-336.
    18. Chan, Wai-Sum & Yang, Hailiang & Zhang, Lianzeng, 2003. "Some results on ruin probabilities in a two-dimensional risk model," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 345-358, July.
    19. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:30:y:2002:i:3:p:297-322. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.