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A solution to the ruin problem for Pareto distributions

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  • Ramsay, Colin M.

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  • Ramsay, Colin M., 2003. "A solution to the ruin problem for Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 109-116, August.
    • Handle: RePEc:eee:insuma:v:33:y:2003:i:1:p:109-116
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    1. Dickson, David C.M. & dos Reis, Alfredo D. Egídio & Waters, Howard R., 1995. "Some Stable Algorithms in Ruin Theory and Their Applications," ASTIN Bulletin, Cambridge University Press, vol. 25(2), pages 153-175, November.
    2. H. Panjer, Harry & Shaun Wang,, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 227-258, November.
    3. Dickson, David C. M., 1989. "Recursive calculation of the probability and severity of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 8(2), pages 145-148, June.
    4. Ramsay, Colin M. & Usabel, Miguel A., 1997. "Calculating Ruin Probabilities via Product Integration," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 263-271, November.
    5. Goovaerts, Marc & de Vylder, Florian, 1984. "A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 14(1), pages 53-59, April.
    6. Thorin, Olof & Wikstad, Nils, 1977. "Calculation of Ruin Probabilities when the Claim Distribution is Lognormal," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 231-246, January.
    7. Embrechts, P. & Villasenor, J. A., 1988. "Ruin estimates for large claims," Insurance: Mathematics and Economics, Elsevier, vol. 7(4), pages 269-274, December.
    8. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    9. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    10. Dickson, David C. M. & Waters, Howard R., 1991. "Recursive Calculation of Survival Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 199-221, November.
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    Cited by:

    1. Su, Wen & Yong, Yaodi, 2024. "Estimating a VaR-type ruin measure by Laguerre series expansion in classical compound Poisson risk model," Statistics & Probability Letters, Elsevier, vol. 205(C).
    2. Danijel Grahovac, 2018. "Densities of Ruin-Related Quantities in the Cramér-Lundberg Model with Pareto Claims," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 273-288, March.
    3. Woo, Jae-Kyung, 2011. "Refinements of two-sided bounds for renewal equations," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 189-196, March.
    4. Olena Ragulina & Jonas Šiaulys, 2020. "Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy," Mathematics, MDPI, vol. 8(11), pages 1-35, October.
    5. Peralta, Oscar & Rojas-Nandayapa, Leonardo & Xie, Wangyue & Yao, Hui, 2018. "Approximation of ruin probabilities via Erlangized scale mixtures," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 136-156.
    6. Martire, Antonio Luciano, 2022. "Volterra integral equations: An approach based on Lipschitz-continuity," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    7. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
    8. Emilio Gómez-Déniz & José María Sarabia & Enrique Calderín-Ojeda, 2019. "Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem," Risks, MDPI, vol. 7(2), pages 1-16, June.
    9. Albrecher, Hansjörg & Kortschak, Dominik, 2009. "On ruin probability and aggregate claim representations for Pareto claim size distributions," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 362-373, December.
    10. Franck Adékambi & Kokou Essiomle, 2020. "Ruin Probability for Stochastic Flows of Financial Contract under Phase-Type Distribution," Risks, MDPI, vol. 8(2), pages 1-21, May.
    11. Michał Brzeziński, 2013. "Robust estimation of the Pareto index: A Monte Carlo Analysis," Working Papers 2013-32, Faculty of Economic Sciences, University of Warsaw.

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