
AIMS Mathematics, 2020, 5(4): 32313255. doi: 10.3934/math.2020208
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Optimal reinsurance for both an insurer and a reinsurer under general premium principles
1 School of Mathematics and Statistics, Shandong Normal University, Jinan, 250358, China
2 School of Mathematical Sciences, University of Jinan, Jinan, 250022, China
Received: , Accepted: , Published:
References
1. K. Borch, An attempt to determine the optimum amount of stop loss reinsurance, In: Transactions of the 16th International Congress of Actuaries, 1 (1960), 597610.
2. P. M. Kahn, Some remarks on a recent paper by Borch. ASTIN Bull., 1 (1961), 265272.
3. K. J. Arrow, Uncertainty and the welfare economics of medical care, Am. Econ. Rev., 53 (1963), 941973.
4. H. U. Gerber, Paretooptimal risk exchanges and related decision problems, ASTIN Bull., 10 (1978), 2533.
5. A. Y. Golubin, Paretooptimal insurance policies in the models with a premium based on the actuarial value, J. Risk Insur., 73 (2006), 469487.
6. N. L. Bowers, H. U. Gerber, J. C. Hickman, et al. Actuarial Mathematics, 2Eds., The Society of Actuaries, Schaumburg, 1997.
7. S. Vajda, Minimum variance reinsurance, ASTIN Bull., 2 (1962), 257260.
8. M. Kaluszka, A. Okolewski, An extension of Arrow's result on optimal reinsurance contract, J. Risk Insur., 75 (2008), 275288.
9. J. Cai, K. S. Tan, Optimal retention for a stoploss reinsurance under the VaR and CTE risk measures, ASTIN Bull., 37 (2007), 93112.
10. J. Cai, K. S. Tan, C. G. Weng, et al. Optimal reinsurance under VaR and CTE risk measures, Insur. Math. Econ., 43 (2008), 185196.
11. K. C. Cheung, Optimal reinsurance revisiteda geometric approach, ASTIN Bull., 40 (2010), 221239.
12. Y. C. Chi, K. S. Tan, Optimal reinsurance under VaR and CVaR risk measures: A simplified approach, ASTIN Bull., 41 (2011), 547574.
13. Y. C. Chi, Optimal reinsurance under variance related premium principles, Insur. Math. Econ., 51 (2012), 310321.
14. Y. C. Chi, K. S. Tan, Optimal reinsurance with general premium principles, Insur. Math. Econ., 52 (2013), 180189.
15. H. H. Huang, Optimal insurance contract under a valueatrisk constraint, Geneva Risk Ins. Rev., 31 (2006), 91110.
16. Z. Y. Lu, L. P. Liu, S. W. Meng, Optimal reinsurance with concave ceded loss functions under VaR and CTE risk measures, Insur. Math. Econ., 52 (2013), 4651.
17. K. S. Tan, C. G. Weng, Y. Zhang, Optimality of general reinsurance contracts under CTE risk measure, Insur. Math. Econ., 49 (2011), 175187.
18. K. Borch, The optimal reinsurance treaties, ASTIN Bull., 5 (1969), 293297.
19. J. Cai, Y. Fang, Z. Li, et al. Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable probability, J. Risk Insur., 80 (2013), 145168.
20. Y. Fang, Z. F. Qu, Optimal combination of quotashare and stoploss reinsurance treaties under the joint survival probability, IMA J. Manag. Math., 25 (2014), 89103.
21. J. Cai, C. Lemieux, F. D. Liu, Optimal reinsurance from the perspectives of both an insurer and a reinsurer, ASTIN Bull., 46 (2016), 815849.
22. A. Lo, A Neyman Pearson perspective on optimal reinsurance with constraints, ASTIN Bull., 47 (2017), 467499.
23. W. J. Jiang, J. D. Ren, R. Zitikis, Optimal reinsurance policies under the VaR risk measure when the interests of both the cedent and the reinsurer are taken into account, Risks, 5 (2017), 122.
24. J. Cai, H. Y. Liu, R. D. Wang, Paretooptimal reinsurance arrangements under general model settings, Insur. Math. Econ., 77 (2017), 2437.
25. Y. Fang, X. Wang, H. L. Liu, et al. Paretooptimal reinsurance for both the insurer and the reinsurer with general premium principles, Commun. StatTheory. M., 48 (2019), 61346154.
26. A. Lo, Z. F. Tang, Paretooptimal reinsurance policies in the presence of individual risk constraints, Ann. Oper. Res., 274 (2019), 395423.
27. Y. X. Huang, C. C. Yin, A unifying approach to constrained and unconstrained optimal reinsurance, J. Comput. Appl. Math., 360 (2019), 117.
28. P. Embrechts, G. Puccetti, Bounds for functions of multivariate risks, J. Multivariate Anal., 97 (2006), 526547.
29. A. J. McNeil, R. Frey, P. Embrechts, Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton University Press, 2005.
30. J. Dhaene, M. Denuit, M. J. Goovaerts, et al. The concept of comonotonicity in actuarial science and finance: Theory, Insur. Math. Econ., 31 (2002), 333.
31. M. Shaked, J. G. Shanthikumar, Stochastic Orders, Springer, 2007.
32. Q. Zhao, Structural learning about directed acyclic graphs from multiple databases, Abstra. Appl. Anala., 2012 (2012), 579543.
33. H. Y. Wang, Z. Wu, Eigenvalues of stochastic Hamiltonian systems driven by Poisson process with boundary conditions, Bound Value Probl., 2017 (2017), 120.
34. X. L. Wang, F. Chen, L. Lin, Empirical likelihood inference for estimating equation with missing data, Sci. China Math., 56 (2013), 12331245.
35. X. L. Wang, Y. Q. Song, L. Lin, Handling estimating equation with nonignorably missing data based on SIR algorithm, J. Comput. Appl. Math., 326 (2017), 6270.
36. C. Hu, Strong laws of large numbers for sublinear expectation under controlled 1st moment condition, Chinese Ann. Math. B, 39 (2018), 791804.
37. C. Hu, Central limit theorems for sublinear expectation under the Lindeberg condition, J. Inequal. Appl., 2018 (2018), 121.
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