Applications of Fuzzy Regression in Actuarial Analysis

Journal of Risk and Insurance

Volumn 70, Issue 4, 2003, Pages 665-699

  De Andrés Sánchez, Jorge ^a   Gómez, Antonio Terceño ^a  

^a UNIVERSITAT ROVIRA I VIRGILI   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0348157104     PISSN: 00224367     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.0022-4367.2003.00070.x     Document Type: Review

References (54)

1. Ang, A., and M. Sherris, 1997, Term Structure Models: A Perspective from the Long Rate, North American Actuarial Journal, 3(3): 122-138.
2. Bababbell, D. F., and C. B. Merrill, 1996, Valuation of Interest-Sensitive Financial Instruments (Schaumburg: Society of Actuaries).
3. Benjamin, S., and L. M. Eagles, 1986, Reserves in Lloyd's and the London Market, Journal of the Institute of Actuaries, 113(2): 197-257.
4. Buckley, J. J., 1987, The Fuzzy Mathematics of Finance, Fuzzy Sets and Systems, 21: 57-73.
5. Buckley, J. J., and Y. Qu, 1990a, Solving Linear and Quadratic Fuzzy Equations, Fuzzy Sets and Systems, 38: 43-59.
6. Buckley, J. J., and Y. Qu, 1990b, On Using α-Cuts to Evaluate Fuzzy Equations, Fuzzy Sets and Systems, 38: 309-312.
7. Buckley, J. J., and Y. Qu, 1990c, Solving Fuzzy Equations: A New Solution Concept, Fuzzy Sets and Systems, 39: 291-301.
8. Carriere, J. F., 1999, Long-Term Yield Rates for Actuarial Valuations, North American Actuarial Journal, 3(3): 13-24.
9. Chambers, D. R., W. T. Carleton, and D. W. Waldman, 1984, A New Approach to Estimation of the Term Structure of Interest Rates, Journal of Financial and Quantitative Analysis, 19: 233-252.
10. Cummins, J. D., 1990, Multi-Period Discounted Cash Flow Rate-Making Models in Property-Liability Insurance, Journal of Risk and Insurance, 57(1): 79-109.
11. Cummins, J. D., and R. A. Derrig, 1993, Fuzzy Trends in Property-Liability Insurance Claim Costs, Journal of Risk and Insurance, 60(3): 429-465.
12. Cummins, J. D., and R. A Derrig, 1997, Fuzzy Financial Pricing of Property-Liability Insurance, North American Actuarial Journal, 1(4): 21-44.
13. de Andrés, J., 2000, Estimating the Temporal Structure of Interest Rates Using Fuzzy Numbers. Application to Financial and Actuarial Valuation and to the Analysis of the Life Insurer's Solvency, Rovira i Virgili University, Unpublished doctoral thesis (in Spanish).
14. Delbaen, F., and S. Lorimier, 1992, Estimation of the Yield Curve and the Forward Rate Curve Starting From a Finite Number of Observations, Insurance: Mathematics and Economics, 11: 259-269.
15. Derrig, R. A., and K. M. Ostaszewski, 1995, Fuzzy Techniques of Pattern Recognition in Risk and Claim Classification, Journal of Risk and Insurance, 62(3): 447-482.
16. Derrig, R. A., and K. M. Ostaszewski, 1997, Managing the Tax Liability of a Property Liability Insurance Company, Journal of Risk and Insurance, 64: 695-711.
17. Devolder, P., 1988, Le taux d'actualisation en assurance, The Geneva Papers on Risk and Insurance, 13: 265-272.
18. Dubois, D., and H. Prade, 1980, Fuzzy Sets and Systems: Theory and Applications (New York: Academic Press).
19. Dubois, D., and H. Prade, 1993, Fuzzy Numbers: An Overview, in: D. Dubois, H. Prade, and R. R. Yager, eds., Fuzzy Sets for Intelligent Systems (San Mateo, Calif.: Morgan Kaufmann Publishers), pp. 113-148.
20. England, P. D., and R. J. Verrall, 1999, Analytic and Bootstrap Estimates of Prediction Errors in Claim Reserving, Insurance: Mathematics and Economics, 25: 281-293.
21. England, P. D., and R. J. Verrall, 2001, A Flexible Framework for Stochastic Claims Reserving, Proceedings of the Casualty Actuarial Society, pp. 1-38.
22. England, P. D., and R. J. Verrall, 2002, Stochastic Claims Reserving in General Insurance, Paper presented to the Institute of Actuaries, Available at http://www.actuaries.org.uk/sessional/sm0201.pdf.
23. Fedrizzi, M., M. Fedrizzi, and W. Ostasiewicz, 1993, Towards Fuzzy Modelling in Economics, Fuzzy Sets and Systems, 54: 259-268.
24. Gerber, H. U., 1995, Life Insurance Mathematics (Heildelberg: Springer).
25. Kaufmann, A., 1986, Fuzzy Subsets Applications in O.R. and Management, in: A. Jones, A. Kaufmann, and H.-J. Zimmermann, eds., Fuzzy Set Theory and Applications (Dordretch: Reidel), pp. 257-300.
26. Kremer, E., 1982, IBNR Claims and the Two-Way of ANOVA, Scandinavian Actuarial Journal, I: 47-55.
27. Lemaire, J., 1990, Fuzzy Insurance, ASTIN Bulletin, 20: 33-55.
28. Li Calzi, M., 1990, Towards a General Setting for the Fuzzy Mathematics of Finance, Fuzzy Sets and Systems, 35: 265-280.
29. Mack, T., 1993, Distribution-Free Calculation of the Standard Error of Chain-Ladder Reserve Estimates, ASTIN Bulletin, 23: 213-223.
30. McCulloch, J. H., 1971, Measuring the Term Structure of Interest Rates, The Journal of Business, 34: 19-31.
31. McCulloch, J. H., 1975, The Tax-Adjusted Yield Curve, Journal of Finance, 30: 811-829.
32. Myers, S.C., and R.A. Cohn, 1987, A Discounted Cash-Flow Approach to Property-Liability Insurance Rate Regulation, in: J. D. Cummins and S. E. Harrington, eds., Fair Rate of Return in Property-Liability Insurance (Norwell, Mass.: Kluwer Academic Publishers).
33. Ostaszewski, K., 1993, An Investigation into Possible Applications of Fuzzy Sets Methods in Actuarial Science (Schaumburg: Society of Actuaries).
34. Profillidis, V. A., B. K. Papadopoulos, and G. N. Botzoris, 1999, Similarities in Fuzzy Regression and Application on Transportation, Fuzzy Economic Review, 4(1): 83-98.
35. Ramenazi, R., and L. Duckstein, 1992, Fuzzy Regression Analysis of the Effect of University Research on Regional Technologies, in: J. Kacprzyk and M. Fedrizzi, eds., Fuzzy Regression Analysis (Heildelberg: Physica-Verlag), pp. 237-263.
36. Ramik, J., and J. Rimanek, 1985, Inequality Relation Between Fuzzy Numbers and its Use in Fuzzy Optimization, Fuzzy Sets and Systems, 16: 123-138.
37. Renshaw, A. E., 1989, Chain-Ladder Modelling and Interactive Modelling (Claims Reserving and GLIM), Journal of the Institute of Actuaries, 116: 559-587.
38. Renshaw, A. E., and R. J. Verrall, 1998, A Stochastic Model Underlying the Chain Ladder Technique, British Actuarial Journal, 4: 903-923.
39. Straub, E., 1997, Non-Life Insurance Mathematics (Berlin: Springer).
40. Tanaka, H., 1987, Fuzzy Data Analysis by Possibilistic Linear Models, Fuzzy Sets and Systems, 24: 363-375.
41. Tanaka, H., and H. Ishibuchi, 1992, A Possibilistic Regression Analysis Based on Linear Programming, in: J. Kacprzyk and M. Fedrizzi, eds., Fuzzy Regression Analysis (Heildelberg: Physica-Verlag), pp. 47-60.
42. Taylor, G. C., 1994, Fair Premium Rating Methods and the Relations Between Them, Journal of Risk and Insurance, 61(4): 592-615.
43. Terceño, A., G. Barberà, J. de Andrés, and C. Belvis, 1996, Fuzzy Methods Incorporated to the Study of Personal Insurances, Fuzzy Economic Review, 1(2): 105-119.
44. Tseng, F.-M., G.-H. Tzeng, H.-C. Yu, and B. J.-C. Yuan, 2001, Fuzzy ARIMA Model for Forecasting the Foreign Exchange Market, Fuzzy Sets and Systems, 118: 9-19.
45. Vasicek, O. A., and H. G. Fong, 1982, Term Structure Modelling Using Exponential Splines, Journal of Finance, 37: 339-349.
46. Verrall, R. J., 1989, A Space State Representation of the Chain Ladder Model, Journal of the Institute of Actuaries, 116: 589-610.
47. Wang, H.-F., and R.-C. Tsaur, 2000, Insight of a Fuzzy Regression Model, Fuzzy Sets and Systems, 112: 355-369.
48. Watada, J., 1992, Fuzzy Time-Series Analysis and Forecasting of Sales Volume, in: J. Kacprzyk and M. Fedrizzi, eds., Fuzzy Regression Analysis (Heildelberg: Physica-Verlag), pp. 211-227.
49. Wright, T. S., 1990, A Stochastic Method for Claims Reserving in General Insurance, Journal of the Institute of Actuaries, 117: 677-731.
50. Yao, Y., 1999, Term Structure Models: A Perspective From the Long Rate, North American Actuarial Journal, 3(3): 122-138.
51. Yen, K. K., S. Ghoshray, and G. Roig, 1999, A Linear Regression Model Using Triangular Fuzzy Number Coefficients, Fuzzy Sets and Systems, 106: 167-177.
52. Young, V. R., 1996, Insurance Rate Changing: A Fuzzy Logic Approach, Journal of Risk and Insurance, 63(3): 461-484.
53. Zadeh, L. A., 1965, Fuzzy Sets, Information and Control, 8: 338-353.
54. Zhao, R., and R. Govind, 1991, Defuzzification of Fuzzy Intervals, Fuzzy Sets and Systems, 43: 45-55.