Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-19T01:47:15.284Z Has data issue: false hasContentIssue false
  • English
  • Français

Fuzzy Insurance

Published online by Cambridge University Press:  29 August 2014

Jean Lemaire
Jean Lemaire*
Affiliation:
Wharton School, University of Pennsylvania, U.S.A.
*
Insurance Department, Wharton School, 3641 Locust Walk, University of Pennsylvania, Philadelphia, PA 19104, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Fuzzy set theory is a recently developed field of mathematics, that introduces sets of objects whose boundaries are not sharply defined. Whereas in ordinary Boolean algebra an element is either contained or not contained in a given set, in fuzzy set theory the transition between membership and non-membership is gradual. The theory aims at modelizing situations described in vague or imprecise terms, or situations that are too complex or ill-defined to be analysed by conventional methods. This paper aims at presenting the basic concepts of the theory in an insurance framework. First the basic definitions of fuzzy logic are presented, and applied to provide a flexible definition of a “preferred policyholder” in life insurance. Next, fuzzy decision-making procedures are illustrated by a reinsurance application, and the theory of fuzzy numbers is extended to define fuzzy insurance premiums.

Keywords

Fuzzy set theorypreferred policyholders in life insuranceoptimal XL-retentionsnet single premiums for pure endowment insurance
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 20 , Issue 1 , April 1990 , pp. 33 - 55
Copyright
Copyright © International Actuarial Association 1990

References

REFERENCES

Aubin, J.P. (1981) Cooperative Fuzzy Games. Math. Oper. Res. 6, 1–13.CrossRefGoogle Scholar
Bellman, R. and Zadeh, L. (1970) Decision-making in a Fuzzy Environment. Management Science 17, B141–B164.CrossRefGoogle Scholar
Buckley, J. (1985) Fuzzy Decision Making with Data: Applications to Statistics. Fuzzy Sets and Systems 16, 139–147.CrossRefGoogle Scholar
Buckley, J. (1987) The Fuzzy Mathematics of Finance. Fuzzy Sets and Systems 21, 257–273.CrossRefGoogle Scholar
Butnariu, D. (1978) Fuzzy Games: A Description of the Concepts. Fuzzy Sets and Systems 1, 181–192.CrossRefGoogle Scholar
Butnariu, D. (1980) Stability and Shapley Value for an n-persons Fuzzy Game. Fuzzy Sets and Systems 4, 63–72.CrossRefGoogle Scholar
Chang, S. (1977) Application of Fuzzy Set Theory to Economics. Kybernetics 6, 203–207.CrossRefGoogle Scholar
Chen, G., Lee, S. and Yu, E. (1980) Application of Fuzzy Set Theory to Economics. In Advances in Fuzzy Sets, Possibility Theory, and Applications, (ed. Wang, P.) pp. 227–305, Plenum Press, New York.Google Scholar
Civanlar, R. and Trussell, J. (1986) Constructing Membership Functions Using Statistical Data. Fuzzy Sets and Systems 18, 1–13.CrossRefGoogle Scholar
Dishkant, H. (1981) About Membership Functions Estimations. Fuzzy Sets and Systems 5, 141–147.CrossRefGoogle Scholar
Dubois, D. and Prade, H. (1978) Operations on Fuzzy Numbers. Int. J. Systems Sci. 9, 613–626.CrossRefGoogle Scholar
Dubois, D. and Prade, H. (1980) Fuzzy Sets and Systems. Academic Press. New York.Google Scholar
Gupta, M., Saridis, G. and Gaines, B., Editors. (1977) Fuzzy Automata and Decision Processes. North Holland, Amsterdam.Google Scholar
Heshmaty, B. and Kander, A. (1985) Fuzzy Linear Regression and its Applications to Forecasting in Uncertain Environment. Fuzzy Sets and Systems 15, 159–191.CrossRefGoogle Scholar
Jajuga, K. (1986) Linear Fuzzy Regression. Fuzzy Sets and Systems, 20, 1986, 343–353.CrossRefGoogle Scholar
Kaufmann, A. (1975) Introduction to the Theory of Fuzzy Subsets. Vol I. Academic Press, New York.Google Scholar
Mathieu-Nicot, B. (1986) Fuzzy Expected Utility. Fuzzy Sets and Systems 19, 163–173.CrossRefGoogle Scholar
Yager, R. and Basson, D. (1976) Decision-making with Fuzzy Sets. Decision Sciences 6, 590–600.CrossRefGoogle Scholar
Zadeh, L. (1965) Fuzzy Sets. Inf. and Control 8, 338–353.CrossRefGoogle Scholar
Zadeh, L., Fu, K., Tanaka, K. and Shimura, M., Editors. (1975) Fuzzy Sets and Their Applications to Cognitive and Decision Processes. Academic Press, New York.Google Scholar
Zimmermann, H-J. (1985) Fuzzy Set Theory and its Applications. Kluwer, Boston.CrossRefGoogle Scholar
Zimmermann, H-J. (1987) Fuzzy Sets, Decision Making and Expert Systems. Kluwer, Boston.CrossRefGoogle Scholar