Weighted pricing functionals with applications to insurance: An overview

North American Actuarial Journal

Volumn 13, Issue 4, 2009, Pages 483-496

  Furman, Edward ^a   Zitikis, Ričardas ^b  

^a YORK UNIVERSITY   (Canada)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951440189     PISSN: 10920277     EISSN: None     Source Type: Journal    
DOI: 10.1080/10920277.2009.10597570     Document Type: Article

References (63)

1. ARNOLD, B. C. 1983. Pareto Distributions. Silver Spring, MD: International Cooperative.
2. ARTZNER, P., F. DELBAEN, J.-M. EBER, and D. Heath. 1999. Coherent Measures of Risk. Mathematical Finance 9(3): 203-28.
3. ASIMIT, A. V., E. FURMAN, and R. Vernic. 2009. On a Multivariate Pareto Distribution. Actuarial Research Group (ARG) Technical Report no. 2009-2. London, Ontario: University of Western Ontario.
4. BRAZAUSKAS, V., B. L. JONES, M. L. PURI, and R. Zitikis. 2008. Estimatinǵ Conditional Tail Expectation with Actuarial Applications in View. Journal of Statistical Planninǵ and Inference 138(11): 3590-3604.
5. BRAZAUSKAS, V., B. L. JONES, and R. Zitikis. 2009. Robust Fittinǵ of Claim Severity Distributions and the Method of Trimmed Moments. Journal of Statistical Planninǵ and Inference 139(6): 2028-43.
6. BUHLMANN, H. 1980. An Economic Premium Principle. ASTINBulletin 11(1): 52-60.
7. BUHLMANN, H. 1984. The General Economic Premium Principle. ASTIN Bulletin 14(1): 13-21.
8. CAI, J., and H. Li. 2005. Conditional Tail Expectations for Multivariate Phase-Type Distributions. Journal of Applied Probability 42(3): 810-925.
9. Chiragiev, A., And Z. Landsman. 2007. Multivariate Pareto Portfolios: TCE-Based Capital Allocation and Divided Differences. Scandi-navian Actuarial Journal 2007(4): 261-80.
10. DENAULT, M. 2001. Coherent Allocation of Risk Capital. Journal of Risk 4(1): 7-21.
11. DENNEBERG, D. 1994. Non-additive Measure and Inteǵral. Dordrecht: Kluwer.
12. DENUIT, M., J. DHAENE, M. GOOVAERTS, and R. KAAS. 2005. Actuarial Theory for Dependent Risks: Measures, Orders and Models. Chichester: Wiley.
13. DEPREZ, O., and H. Gerber. 1985. On Convex Principles of Premium Calculation. Insurance: Mathematics and Economics 4: 179-89.
14. DHAENE, J., M. J. GOOVAERTS, and R. Kaas. 2003. Economic Capital Allocation Derived from Risk Measures. With discussion and authors’ reply. North American Actuarial Journal 7(2): 43-59.
15. DHAENE, J., L. HENRARD, Z. LANDSMAN, A. VANDENDORPE, and S. Vanduffel. 2008. Some Results on the CTE-Based Capital Allocation Rule. Insurance: Mathematics and Economics 42(2): 855-63.
16. FURMAN, E. and Z. LANDSMAN. 2008. Economic Capital Allocations for Non-neǵative Portfolios of Dependent Risks. ASTIN Bulletin 38(2): 601-19.
17. FURMAN, E., and R. Zitikis. 2007. Discussion of “An Actuarial Premium Pricinǵ Model for Nonnormal Insurance and Financial Risks in Incomplete Markets.” North American Actuarial Journal 11(3): 174-76.
18. FURMAN, E., and R. Zitikis 2008a. Weiǵhted Premium Calculation Principles. Insurance: Mathematics and Economics 42(1): 459-65.
19. FURMAN, E., and R. Zitikis 2008b. Weiǵhted Risk Capital Allocations. Insurance: Mathematics and Economics 43(2): 263-69.
20. FURMAN, E., and R. Zitikis 2008c. Monotonicity of Ratios Involvinǵ Incomplete Gamma Functions with Actuarial Applications. Journal of Inequalities in Pure and Applied Mathematics, 9(3): 1-6.
21. FURMAN, E., and R. Zitikis 2008d. A Monotonicity Property of the Composition of Reǵularized and Inverted-Reǵularized Gamma Functions with Applications. Journal of Mathematical Analysis and Applications 348(2): 971-76.
22. FURMAN, E., and R. Zitikis 2009. General Stein-Type Decompositions of Covariances and the Capital Asset Pricinǵ Model. In Pro-ceedinǵs of the 58th Annual Meetinǵ of the Midwest Finance Association, vol. 6, ed. L. E. Blose, Chicaǵo, IL, March 4-7.
23. GERBER, H. U. 1979. An Introduction to Mathematical Risk Theory. Philadelphia: University of Pennsylvania Press.
24. GOOVAERTS, M. J., F. DE VYLDER, and J. HAEZENDONCK. 1984. Insurance Premiums: Theory and Applications. Amsterdam: North-Holland.
25. GOOVAERTS, M. J., R. KAAS, and J. Dhaene. 2003. Economical Capital Allocation Derived from Risk Measures. North American Actuarial Journal 7(2): 44-59.
26. GRESELIN, F., M. L. PURI, and R. Zitikis 2009. L-Functions, Processes, and Statistics in Measurinǵ Economic Inequality and Actuarial Risks. Statistics and Its Interface 2(2): 227-45.
27. HAMADA, M., and E. A. Valdez. 2008. CAPM and Option Pricinǵ with Elliptically Contoured Distributions. Journal of Risk and Insurance 75(2): 387-409.
28. HEILMANN, W.-R. 1989. Decision Theoretic Foundations of Credibility Theory. Insurance: Mathematics and Economics 8(1): 77-95.
29. HESSELAGER, O., and U. ANDERSSON. 2002. Risk Sharinǵ and Risk Capital Allocation. Workinǵ Paper. Ballerup, Denmark: Tryǵ Insurance.
30. HURLIMANN, W. 2001. Analytical Evaluation of Economic Risk Capitals for Portfolio of Gamma Risks. ASTINBulletin 31(1): 107-22.
31. JONES, B. L., and R. Zitikis. 2003. Empirical Estimation of Risk Measures and Related Quantities. North American Actuarial Journal 7(4): 44-54.
32. JORGENSEN, B. 1997. The Theory of Dispersion Models. New York: Chapman and Hall.
33. KAAS, R., A. E. VAN HEERWAARDEN, and M. J. Goovaerts. 1994. Orderinǵ of Actuarial Risks. Brussels: CAIRE Education Series.
34. KALKBRENER, M. 2005. An Axiomatic Approach to Capital Allocation. Mathematical Finance 15(3): 425-37.
35. KAMPS, U. 1998. On a Class of Premium Principles Includinǵ the Esscher Principle. Scandinavian Actuarial Journal 1998(1): 75-80.
36. KIM, H.-T. 2007. Estimation and Allocation of Insurance Risk Capital. Ph.D. thesis. Waterloo, Ontario: University of Waterloo.
37. LANDSMAN, Z., and J. Neslehova. 2008. Stein’s Lemma for Elliptical Random Vectors. Journal of Multivariate Analysis 99(5): 912-27.
38. LANDSMAN, Z., and M. Sherris. 2007. An Actuarial Premium Pricinǵ Model for Nonnormal Insurance and Financial Risks in Incomplete Markets. North American Actuarial Journal 11(1): 119-35.
39. LANDSMAN, Z., and E. Valdez. 2005. Tail Conditional Expectations for Exponential Dispersion Models. ASTIN Bulletin 35(1): 189-209.
40. MEUCCI, A. 2007. Risk and Asset Allocation. Berlin: Sprinǵer.
41. MULLER, H. H. 1987. Economic Premium Principles in Insurance and the Capital Asset Pricinǵ Model. ASTIN Bulletin 17(2): 141-50.
42. NECIR, A., and D. Meraghni. 2009. Empirical Estimation of the Proportional Hazard Premium for Heavy-Tailed Claim Amounts. Insurance: Mathematics and Economics 45: 49-58.
43. NECIR, A., A. RASSOUL, and R. ZITIKIS. 2009. The Actuarial CTE Risk Measure for Heavy-Tailed Losses: A New Estimator and Confidence intervals. Actuarial Research Clearinǵ House, in press.
44. PANJER, H. H. 2002. Measurement of Risk, Solvency Requirements and Allocation of Capital within Financial Conǵlomerates. Institute of Insurance and Pension Research Report 01-15. Waterloo, Ontario: University of Waterloo.
45. PANJER, H. H., and J. Jing. 2001. Solvency and Capital Allocation. Institute of Insurance and Pension Research Report 01-14. Waterloo. Ontario: University of Waterloo.
46. PATIL, G. P., and K. J. Ord. 1976. On Size-Biased Samplinǵ and Related Form-Invariant Weiǵhted Distributions. Sankhyä, Ser. B 38(1): 48-61.
47. PATIL, G. P., and C. R. Rao. 1978. Weiǵhted Distributions and Size-Biased Samplinǵ with Applications to Wildlife Populations and Human Families. Biometrics 34(2): 179-89.
48. PFLUG, G. C., and W. Römisch. 2007. Modeling, Measurinǵ and Manaǵinǵ Risk. Sinǵapore: World Scientific.
49. SCHECHTMAN, E., A. SHELEF, S. YITZHAKI, and R. Zitikis. 2008. Testinǵ Hypotheses about Absolute Concentration Curves and Marǵinal Conditional Stochastic Dominance. Econometric Theory 24(4): 1044-62.
50. TAN, K. S., C. WENG, and Y. ZHANG. 2009. VaR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance. North American Actuarial Journal, 13(4): 20-20.
51. TSANAKAS, A. 2004. Dynamic Capital Allocation with Distortion Risk Measures. Insurance: Mathematics and Economics 35(2): 22343.
52. TSANAKAS, A. 2008. Risk Measurement in the Presence of Backǵround Risk. Insurance: Mathematics and Economics 42(2): 520-28.
53. TSANAKAS, A., and C. Barnett. 2003. Risk Capital Allocation and Cooperative Pricinǵ of Insurance Liabilities. Insurance: Mathematics and Economics 33(2): 239-54.
54. TSANAKAS, A., and N. Christofides. 2006. Risk Exchanǵe with Distorted Probabilities. ASTIN Bulletin 36(1): 219-43.
55. TSANAKAS, A., and E. Desli. 2003. Risk Measures and Theories of Choice. British Actuarial Journal 9(4): 959-91.
56. VENTER, G. G. 2004. Capital Allocation Survey with Commentary. North American Actuarial Journal 8(2): 96-107.
57. VENTER, G. G., J. A. MAYOR, and R. E. Kreps. 2006. Marǵinal Decomposition of Risk Measures. ASTIN Bulletin 36(2): 375-413.
58. VERNIC, R. 2008. Multivariate Skew-Normal Distributions with Applications in Insurance. Insurance: Mathematics and Economics 38(2): 413-26.
59. WANG, S. 1995. Insurance Pricinǵ and Increased Limits Ratemakinǵ by Proportional Hazards Transforms. Insurance: Mathematics and Economics 17(1): 43-54.
60. WANG, S. 1998. An Actuarial Index of the Riǵht-Tail Risk. North American Actuarial Journal 2(2): 88-101.
61. WANG, S. 2007. Normalized Exponential Tilting: Pricinǵ and Measurinǵ Multivariate Risks. North American Actuarial Journal 11(3): 89-99.
62. WANG, S. S., V. R. YOUNG, and H. H. Panjer. 1997. Axiomatic Characterization of Insurance Prices. Insurance: Mathematics and Economics 21(2): 173-83.
63. YOUNG, V. R. 2004. Premium Principles. In Encyclopedia of Actuarial Science, ed. J. L. Teuǵels and B. Sundt. New York: Wiley.