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Multivariate insurance models: An overview

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  • Anastasiadis, Simon
  • Chukova, Stefanka

Abstract

This literature review summarizes the results from a collection of research papers that relate to modeling insurance claims and the processes associated with them. We consider work by more than 55 authors, published or presented between 1971 and 2008.

Suggested Citation

  • Anastasiadis, Simon & Chukova, Stefanka, 2012. "Multivariate insurance models: An overview," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 222-227.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:222-227
    DOI: 10.1016/j.insmatheco.2011.01.013
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    References listed on IDEAS

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    1. Bäuerle, Nicole & Müller, Alfred, 1998. "Modeling and Comparing Dependencies in Multivariate Risk Portfolios," ASTIN Bulletin, Cambridge University Press, vol. 28(1), pages 59-76, May.
    2. Dhaene, Jan & Denuit, Michel, 1999. "The safest dependence structure among risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 11-21, September.
    3. Vernic, Raluca, 2000. "A Multivariate Generalization of the Generalized Poisson Distribution," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 57-67, May.
    4. Ribas, Carme & Marin-Solano, Jesus & Alegre, Antonio, 2003. "On the computation of the aggregate claims distribution in the individual life model with bivariate dependencies," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 201-215, April.
    5. Hu, Taizhong & Wu, Zhiqiang, 1999. "On dependence of risks and stop-loss premiums," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 323-332, May.
    6. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    7. Wang, Guojing & Yuen, Kam C., 2005. "On a correlated aggregate claims model with thinning-dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 456-468, June.
    8. Meng, Qingbin & Zhang, Xin & Guo, Junyi, 2008. "On a risk model with dependence between claim sizes and claim intervals," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1727-1734, September.
    9. Pfeifer, Dietmar & Nešlehová, Johana, 2004. "Modeling and Generating Dependent Risk Processes for IRM and DFA," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 333-360, November.
    10. Vernic, Raluca, 1997. "On The Bivariate Generalized Poisson Distribution," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 23-32, May.
    11. Ambagaspitiya, Rohana S., 1998. "On the distribution of a sum of correlated aggregate claims," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 15-19, October.
    12. Wu, Xueyuan & Yuen, Kam C., 2003. "A discrete-time risk model with interaction between classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 117-133, August.
    13. Cossette, Helene & Gaillardetz, Patrice & Marceau, Etienne & Rioux, Jacques, 2002. "On two dependent individual risk models," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 153-166, April.
    14. Cai, Jun & Li, Haijun, 2005. "Multivariate risk model of phase type," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 137-152, April.
    15. Ambagaspitiya, Rohana S., 1998. "Compound bivariate Lagrangian Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 21-31, October.
    16. Kolev, Nikolai & Paiva, Delhi, 2008. "Random sums of exchangeable variables and actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 147-153, February.
    17. Genest, Christian & Marceau, Etienne & Mesfioui, Mhamed, 2003. "Compound Poisson approximations for individual models with dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 73-91, February.
    18. Frostig, Esther, 2001. "Comparison of portfolios which depend on multivariate Bernoulli random variables with fixed marginals," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 319-332, December.
    19. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 209-238, November.
    20. Bäuerle, Nicole & Grübel, Rudolf, 2005. "Multivariate Counting Processes: Copulas and Beyond," ASTIN Bulletin, Cambridge University Press, vol. 35(2), pages 379-408, November.
    21. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    22. Vernic, Raluca, 1999. "Recursive Evaluation of Some Bivariate Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 315-325, November.
    23. Cossette, Helene & Marceau, Etienne, 2000. "The discrete-time risk model with correlated classes of business," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 133-149, May.
    24. 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.
    25. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2002. "On a correlated aggregate claims model with Poisson and Erlang risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 205-214, October.
    26. Dhaene, J. & Goovaerts, M. J., 1997. "On the dependency of risks in the individual life model," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 243-253, May.
    27. Frostig, Esther, 2001. "A comparison between homogeneous and heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 59-71, August.
    28. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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    Cited by:

    1. Michel Denuit & Anna Kiriliouk & Johan Segers, 2014. "Max-factor individual risk models with application to credit portfolios," Papers 1412.3230, arXiv.org.
    2. Pai, Jeffrey & Ravishanker, Nalini, 2020. "Livestock mortality catastrophe insurance using fatal shock process," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 58-65.
    3. Denuit, Michel & Kiriliouk, Anna & Segers, Johan, 2014. "Max-Factor individual risk models with application to credit portfolios," LIDAM Discussion Papers ISBA 2014048, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Denuit, Michel & Kiriliouk, Anna & Segers, Johan, 2015. "Max-factor individual risk models with application to credit portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 162-172.
    5. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.

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