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Upper and lower bounds for sums of random variables

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Cited by:

  1. KOCH, Inge & DE SCHEPPER, Ann, 2006. "The comonotonicity coefficient: A new measure of positive dependence in a multivariate setting," Working Papers 2006030, University of Antwerp, Faculty of Business and Economics.
  2. Robert, Christian Y., 2013. "Market Value Margin calculations under the Cost of Capital approach within a Bayesian chain ladder framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 216-229.
  3. Cheung, Ka Chun, 2007. "Optimal allocation of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 382-391, November.
  4. Van Weert, Koen & Dhaene, Jan & Goovaerts, Marc, 2010. "Optimal portfolio selection for general provisioning and terminal wealth problems," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 90-97, August.
  5. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers 1402.2492, arXiv.org.
  6. Grzegorz Darkiewicz & Griselda Deelstra & Jan Dhaene & Tom Hoedemakers & Michèle Vanmaele, 2009. "Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 847-866, December.
  7. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
  8. Jianqiang Sun & Langnan Chen & Shiyin Li, 2013. "A Quasi‐Analytical Pricing Model for Arithmetic Asian Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(12), pages 1143-1166, December.
  9. Zhang, Yiying & Zhao, Peng, 2015. "Comparisons on aggregate risks from two sets of heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 124-135.
  10. Pagnoncelli, Bernardo K. & Vanduffel, Steven, 2012. "A provisioning problem with stochastic payments," European Journal of Operational Research, Elsevier, vol. 221(2), pages 445-453.
  11. Alexeev Vitali & Ignatieva Katja & Liyanage Thusitha, 2021. "Dependence Modelling in Insurance via Copulas with Skewed Generalised Hyperbolic Marginals," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(2), pages 1-20, April.
  12. Karel J. in’t Hout & Jacob Snoeijer, 2021. "Numerical Valuation of American Basket Options via Partial Differential Complementarity Problems," Mathematics, MDPI, vol. 9(13), pages 1-17, June.
  13. Antonella Campana, 2007. "On Tail Value-at-Risk for sums of non-independent random variables with a generalized Pareto distribution," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 32(2), pages 169-180, December.
  14. Hua, Lei & Cheung, Ka Chun, 2008. "Stochastic orders of scalar products with applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 865-872, June.
  15. Yang, Yang & Wang, Guojing & Yao, Jing & Xie, Hengyue, 2025. "A generalized tail mean-variance model for optimal capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 157-179.
  16. Denuit, Michel, 2008. "Comonotonic approximations to quantiles of life annuity conditional expected present value," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 831-838, April.
  17. De Schepper, Ann & Goovaerts, Marc & Dhaene, Jan & Kaas, Rob & Vyncke, David, 2002. "Bounds for present value functions with stochastic interest rates and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 87-103, August.
  18. Hua, Lei & Cheung, Ka Chun, 2008. "Worst allocations of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 93-98, August.
  19. Reynaerts, Huguette & Vanmaele, Michele & Dhaene, Jan & Deelstra, Griselda, 2006. "Bounds for the price of a European-style Asian option in a binary tree model," European Journal of Operational Research, Elsevier, vol. 168(2), pages 322-332, January.
  20. Michèle Vanmaele & Griselda Deelstra & Jan Liinev, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," ULB Institutional Repository 2013/7604, ULB -- Universite Libre de Bruxelles.
  21. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.
  22. Xu, Liang & Gao, Chunyan & Kou, Gang & Liu, Qinjun, 2017. "Comonotonic approximation to periodic investment problems under stochastic drift," European Journal of Operational Research, Elsevier, vol. 262(1), pages 251-261.
  23. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
  24. 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.
  25. Afhami, Bahareh & Rezapour, Mohsen & Madadi, Mohsen & Maroufy, Vahed, 2023. "A comonotonic approximation to optimal terminal wealth under a multivariate Merton model with correlated jump risk," Applied Mathematics and Computation, Elsevier, vol. 444(C).
  26. Karel in 't Hout & Jacob Snoeijer, 2021. "Numerical valuation of American basket options via partial differential complementarity problems," Papers 2106.01200, arXiv.org.
  27. Hanbali, Hamza & Dhaene, Jan & Linders, Daniël, 2022. "Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 22-37.
  28. Antonella Campana & Paola Ferretti, 2008. "Bounds for Concave Distortion Risk Measures for Sums of Risks," Springer Books, in: Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods in Insurance and Finance, pages 43-51, Springer.
  29. Annaert, Jan & Deelstra, Griselda & Heyman, Dries & Vanmaele, Michèle, 2007. "Risk management of a bond portfolio using options," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 299-316, November.
  30. Laeven, Roger J.A. & Goovaerts, Marc J. & Hoedemakers, Tom, 2005. "Some asymptotic results for sums of dependent random variables, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 154-172, October.
  31. Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
  32. Griselda Deelstra & Michèle Vanmaele & David Vyncke, 2010. "Minimizing the Risk of a Financial Product Using a Put Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(4), pages 767-800, December.
  33. Yulian Fan & Huadong Zhang, 2017. "The pricing of average options with jump diffusion processes in the uncertain volatility model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-31, March.
  34. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2011. "Worst case risk measurement: Back to the future?," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 380-392.
  35. Magnus Carlehed, 2023. "A Model for Risk Adjustment (IFRS 17) for Surrender Risk in Life Insurance," Risks, MDPI, vol. 11(3), pages 1-22, March.
  36. Bahl, Raj Kumari & Sabanis, Sotirios, 2021. "Model-independent price bounds for Catastrophic Mortality Bonds," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 276-291.
  37. Mesfioui, Mhamed & Denuit, Michel, 2014. "Comonotonicity, orthant convex order and sums of random variables," LIDAM Discussion Papers ISBA 2014002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  38. Alexandre Petkovic, 2009. "Three essays on exotic option pricing, multivariate Lévy processes and linear aggregation of panel models," ULB Institutional Repository 2013/210357, ULB -- Universite Libre de Bruxelles.
  39. Griselda Deelstra & Alexandre Petkovic & Michèle Vanmaele, 2008. "Pricing and Hedging Asian Basket Spread Options," Working Papers ECARES 2008_004, ULB -- Universite Libre de Bruxelles.
  40. Deelstra, G. & Liinev, J. & Vanmaele, M., 2004. "Pricing of arithmetic basket options by conditioning," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 55-77, February.
  41. Ying Zhang & Chuancun Yin, 2014. "A new multivariate dependence measure based on comonotonicity," Papers 1410.7845, arXiv.org.
  42. Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
  43. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
  44. Margherita Doria & Elisa Luciano & Patrizia Semeraro, 2022. "Machine learning techniques in joint default assessment," Papers 2205.01524, arXiv.org, revised Sep 2023.
  45. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Ruodu Wang, 2017. "Risk bounds for factor models," Finance and Stochastics, Springer, vol. 21(3), pages 631-659, July.
  46. M. Goovaerts & A. De Schepper & Y. Hua & G. Darkiewicz & D: Vyncke, 2005. "On the Use of Copulas for Calculating the Present Value of a General Cash Flow," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(1), pages 69-94.
  47. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
  48. Dhaene, J. & Henrard, L. & Landsman, Z. & Vandendorpe, A. & Vanduffel, S., 2008. "Some results on the CTE-based capital allocation rule," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 855-863, April.
  49. Landsman, Zinoviy & Pat, Nika & Dhaene, Jan, 2013. "Tail Variance premiums for log-elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 441-447.
  50. J. Marin-Solano (Universitat de Barcelona) & O. Roch (Universitat de Barcelona) & J. Dhaene (Katholieke Univerisiteit Leuven) & C. Ribas (Universitat de Barcelona) & M. Bosch-Princep (Universitat de B, 2009. "Buy-and-Hold Strategies and Comonotonic Approximations," Working Papers in Economics 213, Universitat de Barcelona. Espai de Recerca en Economia.
  51. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2015. "Comonotonic Monte Carlo and its applications in option pricing and quantification of risk," Documents de travail du Centre d'Economie de la Sorbonne 15015, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  52. D. Vyncke & M. Goovaerts & J. Dhaene & S. Vanduffel, 2005. "Optimal Portfolio Selection for Cash-Flows with Bounded Capital at Risk," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(1), pages 103-114.
  53. Hoedemakers, Tom & Darkiewicz, Grzegorz & Goovaerts, Marc, 2005. "Approximations for life annuity contracts in a stochastic financial environment," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 239-269, October.
  54. Hürlimann, Werner, 2010. "Analytical Pricing of the Unit-Linked Endowment with Guarantees and Periodic Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 631-653, November.
  55. Hanbali, Hamza & Dhaene, Jan & Linders, Daniël, 2022. "Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 22-37.
  56. Hoedemakers, Tom & Beirlant, Jan & Goovaerts, Marc J. & Dhaene, Jan, 2003. "Confidence bounds for discounted loss reserves," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 297-316, October.
  57. Antonella Campana & Paola Ferretti, 2005. "Distortion Risk Measures and Discrete Risks," Game Theory and Information 0510013, University Library of Munich, Germany.
  58. Hobson, David & Laurence, Peter & Wang, Tai-Ho, 2005. "Static-arbitrage optimal subreplicating strategies for basket options," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 553-572, December.
  59. Brückner, Karsten, 2008. "Quantifying the error of convex order bounds for truncated first moments," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 261-270, February.
  60. Li, Xiaohu & You, Yinping, 2012. "On allocation of upper limits and deductibles with dependent frequencies and comonotonic severities," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 423-429.
  61. Denuit, Michel & Dhaene, Jan & Ribas, Carmen, 2001. "Does positive dependence between individual risks increase stop-loss premiums?," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 305-308, June.
  62. Vanmaele, Michele & Deelstra, Griselda & Liinev, Jan, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 343-367, October.
  63. Laeven, Roger J.A., 2009. "Worst VaR scenarios: A remark," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 159-163, April.
  64. Vanduffel, Steven & Shang, Zhaoning & Henrard, Luc & Dhaene, Jan & Valdez, Emiliano A., 2008. "Analytic bounds and approximations for annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1109-1117, June.
  65. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
  66. Liu, Xiaoming & Jang, Jisoo & Mee Kim, Sun, 2011. "An application of comonotonicity theory in a stochastic life annuity framework," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 271-279, March.
  67. Cheung, Ka Chun, 2008. "Improved convex upper bound via conditional comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 651-655, April.
  68. Peter Laurence & Tai-Ho Wang, 2008. "Distribution-free upper bounds for spread options and market-implied antimonotonicity gap," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 717-734.
  69. Vanduffel, S. & Dhaene, J. & Goovaerts, M. & Kaas, R., 2003. "The hurdle-race problem," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 405-413, October.
  70. Landsman, Zinoviy & Vanduffel, Steven, 2011. "Bounds for some general sums of random variables," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 382-391, March.
  71. Cheung, Ka Chun, 2006. "Optimal portfolio problem with unknown dependency structure," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 167-175, February.
  72. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
  73. Wan-Ni Lai & Yi-Ting Chen & Edward W. Sun, 2021. "Comonotonicity and low volatility effect," Annals of Operations Research, Springer, vol. 299(1), pages 1057-1099, April.
  74. Zheng-wen Wang & Ling Tian, 2016. "How much catastrophe insurance fund needed in China for the ‘big one’? An estimation with comonotonicity method," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(1), pages 55-68, October.
  75. Mesfioui, Mhamed & Denuit, Michel M., 2015. "Comonotonicity, orthant convex order and sums of random variables," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 356-364.
  76. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
  77. Bahareh Afhami & Mohsen Rezapour & Mohsen Madadi & Vahed Maroufy, 2021. "Dynamic investment portfolio optimization using a Multivariate Merton Model with Correlated Jump Risk," Papers 2104.11594, arXiv.org.
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