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Recursive Evaluation of a Family of Compound Distributions

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Cited by:

  1. Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
  2. Rulliere, Didier & Loisel, Stephane, 2004. "Another look at the Picard-Lefevre formula for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 187-203, October.
  3. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
  4. Janecskó, Balázs, 2002. "Portfóliószemléletű hitelkockázat szimulációs meghatározása [Simulated determination of credit risk in portfolio terms]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 664-676.
  5. Denuit, M. & Robert, C.Y., 2020. "Ultimate behavior of conditional mean risk sharing for independent compound Panjer-Katz sums with gamma and Pareto severities," LIDAM Discussion Papers ISBA 2020014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  6. Papalamprou, Konstantinos & Antoniou, Paschalis, 2019. "Estimation of capital requirements in downturn conditions via the CBV model: Evidence from the Greek banking sector," Operations Research Perspectives, Elsevier, vol. 6(C).
  7. Frank Schlottmann & Detlef Seese, 2002. "Hybrid multi-objective evolutionary computation of constrained downside risk-return efficient sets for credit portfolios," Computing in Economics and Finance 2002 78, Society for Computational Economics.
  8. Denuit, Michel & Lefevre, Claude, 1997. "Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 197-213, October.
  9. Sundt, Bjorn, 2003. "Some recursions for moments of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 487-496, December.
  10. Cardoso, Rui M. R. & R. Waters, Howard, 2003. "Recursive calculation of finite time ruin probabilities under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 659-676, December.
  11. Franco-Arbeláez, Luis Ceferino & Franco-Ceballos, Luis Eduardo & Murillo-Gómez, Juan Guillermo & Venegas-Martínez, Francisco, 2015. "Riesgo operativo en el sector salud en Colombia [Operational Risk in the Health Sector in Colombia]," MPRA Paper 63149, University Library of Munich, Germany.
  12. Minkova, Leda D. & Balakrishnan, N., 2014. "Type II bivariate Pólya–Aeppli distribution," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 40-49.
  13. Finner, H. & Kern, P. & Scheer, M., 2015. "On some compound distributions with Borel summands," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 234-244.
  14. Hesselager, Ole, 1995. "Order relations for some distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 129-134, May.
  15. Hahn, G.J. & Leucht, A., 2015. "Managing inventory systems of slow-moving items," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 543-550.
  16. Maria Stefanova, 2012. "Recovery Risiko in der Kreditportfoliomodellierung," Springer Books, Springer, number 978-3-8349-4226-5, June.
  17. Duarte-López, Ariel & Pérez-Casany, Marta & Valero, Jordi, 2020. "The Zipf–Poisson-stopped-sum distribution with an application for modeling the degree sequence of social networks," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
  18. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2009. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 374-381, December.
  19. J. D. Opdyke, 2014. "Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness," Papers 1406.0389, arXiv.org, revised Nov 2014.
  20. Govorun, Maria & Latouche, Guy & Loisel, Stéphane, 2015. "Phase-type aging modeling for health dependent costs," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 173-183.
  21. Caroline Hillairet & Ying Jiao, 2017. "Pricing formulae for derivatives in insurance using the Malliavin calculus," Working Papers 2017-75, Center for Research in Economics and Statistics.
  22. Venegas-Martínez, Francisco & Franco-Arbeláez, Luis Ceferino & Franco-Ceballos, Luis Eduardo & Murillo-Gómez, Juan Guillermo, 2015. "Riesgo operativo en el sector salud en Colombia: 2013," eseconomía, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(43), pages 7-36, segundo s.
  23. Jordi Valero & Josep Ginebra & Marta Pérez-Casany, 2012. "Extended Truncated Tweedie-Poisson Model," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 811-829, September.
  24. A.Hernández-Bastida & J. M. Pérez–Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model: The Net Premium Principle With Exponential Poisson And Gamma–Gamma Distributions," FEG Working Paper Series 07/03, Faculty of Economics and Business (University of Granada).
  25. Shaun S. Wang & Ulrik Franke, 2020. "Enterprise IT service downtime cost and risk transfer in a supply chain," Operations Management Research, Springer, vol. 13(1), pages 94-108, June.
  26. 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.
  27. Anh Ninh, 2021. "Robust newsvendor problems with compound Poisson demands," Annals of Operations Research, Springer, vol. 302(1), pages 327-338, July.
  28. Cordelia Rudolph & Uwe Schmock, 2020. "Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion," Risks, MDPI, vol. 8(2), pages 1-31, May.
  29. Schlottmann, Frank & Seese, Detlef, 2004. "A hybrid heuristic approach to discrete multi-objective optimization of credit portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 373-399, September.
  30. Aleksandr Beknazaryan & Peter Adamic, 2022. "On a stochastic order induced by an extension of Panjer’s family of discrete distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 67-91, January.
  31. Anna Castañer & M. Mercè Claramunt, 2019. "Equilibrium Distributions and Discrete Schur-constant Models," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 449-459, June.
  32. Sundt, Bjorn, 2000. "The multivariate De Pril transform," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 123-136, August.
  33. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
  34. Loisel, Stéphane & Mazza, Christian & Rullière, Didier, 2008. "Robustness analysis and convergence of empirical finite-time ruin probabilities and estimation risk solvency margin," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 746-762, April.
  35. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2015. "A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model," Post-Print hal-00853680, HAL.
  36. Hipp, Christian, 2006. "Speedy convolution algorithms and Panjer recursions for phase-type distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 176-188, February.
  37. S. Chadjiconstantinidis & M. V. Koutras & F. S. Milienos, 2023. "The distribution of extended discrete random sums and its application to waiting time distributions," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
  38. Yang, Jingping & Zhou, Shulin & Zhang, Zhenyong, 2005. "The compound Poisson random variable's approximation to the individual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 57-77, February.
  39. 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.
  40. Vasileios M. Koutras & Markos V. Koutras, 2020. "Exact Distribution of Random Order Statistics and Applications in Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1539-1558, December.
  41. 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.
  42. Frey, Andreas & Schmidt, Volker, 1996. "Taylor-series expansion for multivariate characteristics of classical risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 18(1), pages 1-12, May.
  43. Gillen, David & Hasheminia, Hamed, 2013. "Estimating the demand responses for different sizes of air passenger groups," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 24-38.
  44. Caroline Hillairet & Ying Jiao & Anthony Réveillac, 2017. "Pricing formulae for derivatives in insurance using the Malliavin calculus ," Working Papers hal-01561987, HAL.
  45. Bolance, Catalina & Guillen, Montserrat & Nielsen, Jens Perch, 2003. "Kernel density estimation of actuarial loss functions," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 19-36, February.
  46. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
  47. Eric Ghysels & Christian Gouriéroux & Joann Jasiak, 1995. "Market Time and Asset Price Movements Theory and Estimation," CIRANO Working Papers 95s-32, CIRANO.
  48. Lauer Alexandra & Zähle Henryk, 2016. "Nonparametric estimation of risk measures of collective risks," Statistics & Risk Modeling, De Gruyter, vol. 32(2), pages 89-102, March.
  49. Muneya Matsui, 2017. "Prediction of Components in Random Sums," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 573-587, June.
  50. Li Qin & Susan M. Pitts, 2012. "Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 919-936, December.
  51. 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.
  52. Baena-Mirabete, S. & Puig, P., 2020. "Computing probabilities of integer-valued random variables by recurrence relations," Statistics & Probability Letters, Elsevier, vol. 161(C).
  53. Nabil Kazi-Tani, 2020. "Indifference Pricing of Reinsurance with Reinstatements Using Coherent Monetary Criteria," Working Papers hal-01742638, HAL.
  54. Yuki Itoh, 2008. "Recovery Process Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(3), pages 307-347, December.
  55. Chaubey, Yogendra P. & Garrido, Jose & Trudeau, Sonia, 1998. "On the computation of aggregate claims distributions: some new approximations," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 215-230, December.
  56. Caroline Hillairet & Ying Jiao & Anthony Réveillac, 2018. "Pricing formulae for derivatives in insurance using the Malliavin calculus ," Post-Print hal-01561987, HAL.
  57. Usabel, Miguel A., 1998. "Applications to risk theory of a Monte Carlo multiple integration method," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 71-83, October.
  58. Jae-Kyung Woo & Haibo Liu, 2018. "Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1285-1318, December.
  59. Cardoso, Rui M. R. & Egidio dos Reis, Alfredo D., 2002. "Recursive calculation of time to ruin distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 219-230, April.
  60. Martin Bøgsted & Susan Pitts, 2010. "Decompounding random sums: a nonparametric approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 855-872, October.
  61. Yacine Koucha & Alfredo D. Egidio dos Reis, 2021. "Approximations to ultimate ruin probabilities with a Wienner process perturbation," Papers 2107.02537, arXiv.org.
  62. P. Del Moral & G. W. Peters & Ch. Verg'e, 2012. "An introduction to particle integration methods: with applications to risk and insurance," Papers 1210.3851, arXiv.org, revised Oct 2012.
  63. Eisele, Karl-Theodor, 2006. "Recursions for compound phase distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 149-156, February.
  64. Filippo Curti & Ibrahim Ergen & Minh Le & Marco Migueis & Rob T. Stewart, 2016. "Benchmarking Operational Risk Models," Finance and Economics Discussion Series 2016-070, Board of Governors of the Federal Reserve System (U.S.).
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  66. Shota Gugushvili & Ester Mariucci & Frank van der Meulen, 2020. "Decompounding discrete distributions: A nonparametric Bayesian approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 464-492, June.
  67. Brendan P. M. McCabe & Christopher L. Skeels, 2020. "Distributions You Can Count On …But What’s the Point?," Econometrics, MDPI, vol. 8(1), pages 1-36, March.
  68. Kitano, Masashi & Shimizu, Kunio & Ong, S.H., 2005. "The generalized Charlier series distribution as a distribution with two-step recursion," Statistics & Probability Letters, Elsevier, vol. 75(4), pages 280-290, December.
  69. Yves L. Grize, 2015. "Applications of Statistics in the Field of General Insurance: An Overview," International Statistical Review, International Statistical Institute, vol. 83(1), pages 135-159, April.
  70. Bae, Taehan & Kim, Changki & Kulperger, Reginald J., 2009. "Securitization of motor insurance loss rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 48-58, February.
  71. Marios N. Kyriacou, 2015. "Credit Risk Measurement in Financial Institutions: Going Beyond Regulatory Compliance," Cyprus Economic Policy Review, University of Cyprus, Economics Research Centre, vol. 9(1), pages 31-72, June.
  72. Anastasiadis, Simon & Chukova, Stefanka, 2012. "Multivariate insurance models: An overview," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 222-227.
  73. Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
  74. 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.
  75. James D. Englehardt & Chengjun Peng, 1996. "A Bayesian Benefit‐Risk Model Applied to the South Florida Building Code," Risk Analysis, John Wiley & Sons, vol. 16(1), pages 81-91, February.
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  77. Gómez–Déniz, E. & Pérez–Rodríguez, J.V., 2019. "Modelling distribution of aggregate expenditure on tourism," Economic Modelling, Elsevier, vol. 78(C), pages 293-308.
  78. 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.
  79. Emilio Gómez-Déniz & Jorge V. Pérez-Rodríguez & Simón Sosvilla-Rivero, 2022. "Analyzing How the Social Security Reserve Fund in Spain Affects the Sustainability of the Pension System," Risks, MDPI, vol. 10(6), pages 1-17, June.
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  81. Willmot, Gordon E., 1997. "Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 25-42, October.
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  83. Vasileios M. Koutras & Markos V. Koutras & Spiros D. Dafnis, 2022. "A Family of Induced Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1833-1848, September.
  84. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October.
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  90. 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.
  91. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2014. "A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model," Working Papers hal-00853680, HAL.
  92. Franck Adékambi, 2019. "Moments Of Phase-Type Aging Modeling For Health Dependent Costs," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 37-64, June.
  93. Anna Castañer & M Mercè Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Working Papers hal-01593552, HAL.
  94. Xiaolin Luo & Pavel V. Shevchenko & John B. Donnelly, 2009. "Addressing the Impact of Data Truncation and Parameter Uncertainty on Operational Risk Estimates," Papers 0904.2910, arXiv.org.
  95. Raluca Vernic, 2018. "On the Evaluation of the Distribution of a General Multivariate Collective Model: Recursions versus Fast Fourier Transform," Risks, MDPI, vol. 6(3), pages 1-14, August.
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