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Recursive Evaluation of a Family of Compound Distributions

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Cited by:

  1. 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.
  2. Caroline Hillairet & Ying Jiao & Anthony R'eveillac, 2017. "Pricing formulae for derivatives in insurance using the Malliavin calculus," Papers 1707.05061, arXiv.org.
  3. 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.
  4. 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.
  5. Sandhya E & Latha C M, 2019. "Compound Extended Geometric Distribution and Some of Its Properties," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(3), pages 1-96, November.
  6. Somya Mehra & Peter G. Taylor, 2023. "Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals," Queueing Systems: Theory and Applications, Springer, vol. 105(3), pages 171-187, December.
  7. Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
  8. Anastasiadis, Simon & Chukova, Stefanka, 2012. "Multivariate insurance models: An overview," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 222-227.
  9. Anna Casta~ner & M Merc`e Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Papers 1709.09955, arXiv.org.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Mejdoub, Hanène & Ben Arab, Mounira, 2018. "Impact of dependence modeling of non-life insurance risks on capital requirement: D-Vine Copula approach," Research in International Business and Finance, Elsevier, vol. 45(C), pages 208-218.
  17. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
  18. 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.
  19. Caroline Hillairet & Ying Jiao & Anthony Réveillac, 2017. "Pricing formulae for derivatives in insurance using the Malliavin calculus ," Working Papers hal-01561987, HAL.
  20. Ghysels, E. & Gourieroux, C. & Jasiak, J., 1995. "Market Time and Asset Price Movements: Theory and Estimation," Cahiers de recherche 9536, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  21. Sundt, Bjorn, 2003. "Some recursions for moments of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 487-496, December.
  22. Maria Stefanova, 2012. "Recovery Risiko in der Kreditportfoliomodellierung," Springer Books, Springer, number 978-3-8349-4226-5, March.
  23. 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.
  24. 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.
  25. Yacine Koucha & Alfredo D. Egidio dos Reis, 2021. "Approximations to ultimate ruin probabilities with a Wienner process perturbation," Papers 2107.02537, arXiv.org.
  26. 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.
  27. repec:jss:jstsof:25:i07 is not listed on IDEAS
  28. Hung, Yi-Feng & Lee, Tzu-Yuan, 2010. "Capacity rationing decision procedures with order profit as a continuous random variable," International Journal of Production Economics, Elsevier, vol. 125(1), pages 125-136, May.
  29. Caroline Hillairet & Ying Jiao & Anthony Réveillac, 2018. "Pricing formulae for derivatives in insurance using the Malliavin calculus ," Post-Print hal-01561987, HAL.
  30. 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.
  31. J. F. Walhin, 2003. "Bivariate Hofmann distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(9), pages 1033-1046.
  32. 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.
  33. den Iseger, P. W. & Smith, M. A. J. & Dekker, R., 1997. "Computing compound distributions faster!," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 23-34, June.
  34. 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.
  35. 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.
  36. Gómez–Déniz, E. & Pérez–Rodríguez, J.V., 2019. "Modelling distribution of aggregate expenditure on tourism," Economic Modelling, Elsevier, vol. 78(C), pages 293-308.
  37. 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.
  38. 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.
  39. 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.
  40. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
  41. 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.
  42. 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.
  43. Gómez-Déniz, Emilio & Sarabia, José María & Calderín-Ojeda, Enrique, 2011. "A new discrete distribution with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 406-412, May.
  44. 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.
  45. 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).
  46. 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.
  47. 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.
  48. 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.
  49. 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.
  50. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
  51. 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.
  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. Muneya Matsui, 2017. "Prediction of Components in Random Sums," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 573-587, June.
  54. 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.
  55. 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).
  56. 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.
  57. 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.
  58. 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.
  59. Minkova, Leda D. & Balakrishnan, N., 2014. "Type II bivariate Pólya–Aeppli distribution," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 40-49.
  60. Alexandre Kurth & Dirk Tasche, 2002. "Credit Risk Contributions to Value-at-Risk and Expected Shortfall," Papers cond-mat/0207750, arXiv.org, revised Nov 2002.
  61. Sundt, Bjorn, 2000. "The multivariate De Pril transform," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 123-136, August.
  62. Anh Ninh, 2021. "Robust newsvendor problems with compound Poisson demands," Annals of Operations Research, Springer, vol. 302(1), pages 327-338, July.
  63. 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.
  64. Dhaene, Jan & Vandebroek, Martina, 1995. "Recursions for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 31-38, April.
  65. 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.
  66. 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.
  67. Anna Castañer & M Mercè Claramunt, 2017. "Equilibrium distributions and discrete Schur-constant models," Working Papers hal-01593552, HAL.
  68. 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.
  69. 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).
  70. 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.
  71. Hesselager, Ole, 1995. "Order relations for some distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 129-134, May.
  72. 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).
  73. 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.
  74. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.
  75. 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.
  76. 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.
  77. 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.
  78. 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.
  79. 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.
  80. 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.
  81. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Jing Yao, 2017. "How robust is the value-at-risk of credit risk portfolios?," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 507-534, May.
  82. 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.
  83. 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.
  84. 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.
  85. 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.
  86. 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.
  87. Alessandro Barbiero & Asmerilda Hitaj, 2023. "Discrete approximations of continuous probability distributions obtained by minimizing Cramér-von Mises-type distances," Statistical Papers, Springer, vol. 64(5), pages 1669-1697, October.
  88. 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.
  89. Eisele, Karl-Theodor, 2006. "Recursions for compound phase distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 149-156, February.
  90. J. D. Opdyke, 2014. "Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness," Papers 1406.0389, arXiv.org, revised Nov 2014.
  91. 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.
  92. 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.
  93. 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.
  94. 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.
  95. 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.
  96. 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.
  97. 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.
  98. 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.).
  99. 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.
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