Abstract
Actuarial science encompasses all types of quantifications of risks under conditions of uncertainty for the purpose of setting insurance premiums and reserves. Traditional actuarial methodologies have been built upon probabilistic models, and are often driven by stringent regulation of the insurance business. Deregulation and global competition of the last two decades have opened the door for new methodologies, among them being fuzzy methods. Here we present the uses of fuzzy sets in areas such as: underwriting, risk classification, interest rates, ratemaking, valuation of premium and taxes. We also discuss new opportunities for expanding fuzzy sets methodologies in actuarial science.
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References
Asay, Michael R., Peter R. Bouyoucos, and Anthony Marciano, (1993), “An Economic Approach to Valuation of Single Premium Deferred Annuities,” Financial Optimization, edited by S.A. Zenios, Cambridge University Press, 101–131.
Babad, Y. and Berliner, B., (1994), “The Use of Intervals of Possibilities to Measure and Evaluate Financial Risk and Uncertainty,” 4th AFIR Conference Proceedings, International Actuarial Association, April 20–22, (Orlando), 14: 111–140.
Babbel, David F., and Robert Stricker, (1987), “Asset-Liability Management for Insurers”, in: Insurance Perspectives, Goldman Sachs, May.
Bezdek, J.C., (1981), Pattern Recognition with Fuzzy Objective Function Algorithms, New York, Plenum Press.
Black, Jr., Kenneth, and Skipper, Jr., Harold, (1994), Life Insurance (Twelfth Edition), Prentice-Hall Simon & Schuster.
Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.C., and Nesbitt, C.J., (1986), Actuarial Mathematics, Society of Actuaries, Schaumburg, Illinois.
Brockett, P.L., Xia, X. and Derrig, R.A., (1998), “Using Kohonen’s Self-Organizing Feature Map to Uncover Automobile Bodily Injury Claims Fraud,” Journal of Risk and Insurance, 65–2:245–274.
Buckley, J.J., (1986), “Portfolio analysis using possibility distributions”: Approximate Reasoning in Intelligent System Decision and Control: Proceedings of the International Conference, 69–76, January 8–10, edited by Sanchez, E., and Zadeh, L. A., Pergamon Press, Elmsford, New York.
Buckley, J.J., (1987), “The Fuzzy Mathematics of Finance,” Fuzzy Sets and Systems, 21: 257–273.
Calzi, M.L., (1990), “Towards a General Setting for the Fuzzy Mathematics of Finance,” Fuzzy Sets and Systems, 35:265–280.
Casualty Actuarial Society, (1990), Foundations of Casualty Actuarial Science, R&S Financial Printing, New York.
Conger, R.F., (1984), “The Construction of Automobile Rating Territories in Massachusetts”, Proceedings of the Casualty Actuarial Society, May, 74(141):74.
Cox, Earl, (1995) “A Fuzzy System for Detecting Anomalous Behaviors in Healthcare Provider Claims”, Intelligent Systems for Finance and Business, edited by S. Goonatilake and P. Treleven, John Wiley & Sons, 111–135.
Cummins, J. D. and Grace, Elizabeth, (1994), “Tax Management and Investment Strategies of Property-Liability Insurers,” Journal of Banking and Finance, 18:43–72.
Cummins, J.D. and Derrig, Richard A., (1993), “Fuzzy Trends in Property-Liability Insurance Claim Costs,” Journal of Risk and Insurance, September, 60:429–465.
Cummins, J.D. and Derrig, Richard A., (1997), “Fuzzy Financial Pricing of Property-Liability Insurance,” North American Actuarial Journal, October, 1:21–44.
Derrig, Richard A. and Weisberg, Herbert I., (1998) “AIB PIP Claim Screening Experiment Final Report, Understanding and Improving the Claim Investigation Process”, Massachusetts Fraudulent Claims Payment Filing, DOI Docket R98-41, Boston.
Derrig, Richard A. and Ostaszewski, Krzysztof M., (1997), “Managing the Tax Liability of a Property-Casualty Insurance Company”, Journal of Risk and Insurance, 64–4:696–711.
Derrig, Richard A. and Ostaszewski, Krzysztof M., (1995), “Fuzzy Techniques of Pattern Recognition in Risk and Claim Classification, Journal of Risk and Insurance, 62–3:447–483.
Derrig, Richard A., (1994), “Theoretical Considerations of the Effect of Federal Income Taxes on Investment Income in Property-Liability Ratemaking,” Journal of Risk and Insurance, 61–4:691–709.
Derrig, Richard A., (1993), “Price Regulation in U.S. Automobile Insurance, A Case Study of Massachusetts Private Passenger Automobile Insurance 1978–1990, The Geneva Papers on Risk and Insurance, 18:158–173.
Derrig, Richard A., (1990), “The Development of Property-Liability Insurance Pricing Models in the United States 1969–1989,” Ist AFIR Conference Proceedings, International Actuarial Association, May 23–26, 1990 (Paris), 4:237–264. Reprinted in Casualty Actuarial Society Actuarial Forum, Fall 1991, 19–46.
DeWit, G.W., (1982) “Underwriting and Uncertainty,” Insurance: Mathematics and Economics, 1:277–285.
Dicke, A.A., Bergquist, W., Clancy, R.P., Miller, R.A. III, Panjer, Harry H., Peterson, D.M., Watson, C.B.H., and Luckner, Warren, (1991), Principles of Actuarial Science, by the Society of Actuaries Committee of Actuarial Principles, accepted by the Board of Governors of the Society of Actuaries in October.
Dufresne, Daniel, (1992), “On Discounting when Rates of Return are Random,” Proceedings of Twenty Fourth International Congress of Actuaries, 1:27–43.
Ebanks, Bruce, Karwowski, Waldemar, and Ostaszewski, Krzysztof M., (1992), “Application of Measures of Fuzziness to Risk Classification in Insurance,” Computing and Information, IEEE Computer Society Press, Los Alamitos, California, 290–291
Erbach, David W., (1990) “The Use of Expert Systems to do Risk Analysis,” Intelligent Systems in Business, Edited by Richardson and DeFries, Ablex Publishing Co., New Jersey.
Erbach, David W., and Seah, Eric, (1993), Discussion of “The Application of Fuzzy Sets to Group Health Underwriting” Virginia R. Young, Transactions of the Society of Actuaries 45:585–587.
Frees, E.W., (1990), “Stochastic Life Contingencies with Solvency Considerations,” Transactions of the Society of Actuaries, 42:91–129.
Fuhrer, C. S., (1993), “Credibility Theory,” Record of the Society of Actuaries 19(1B):863–881.
Horgby, Per-Johan, (1998), “Risk Classification By Fuzzy Inference”, The Geneva Papers on Risk and Insurance Theory, 23:63–82.
Horgby, Per-Johan, Lohse, Ralf, and Sittaro, Nocola-Alexander, (1997), “Fuzzy Underwriting: An Application of Fuzzy Logic to Medical Underwriting”, Journal of Actuarial Practice, 5:1–79–105.
Insurance Research Council (1997), Fighting Fraud in the Insurance Industry, 2nd Edition., Wheaton, Il.
Kandel, A., (1982), Fuzzy Techniques in Pattern Recognition, John Wiley and Sons, New York.
Karwowski, Waldemar, and Ostaszewski, Krzysztof M., (1992), “An Analysis of Possible Applications of Fuzzy Set Theory to the Actuarial Credibility Theory,” Proceeding of the Annual Meeting of the North American Fuzzy Information Processing Society, Puerto Vallarta, December.
Karwowski, Waldemar, and Ostaszewski, Krzysztof M., (1993), “Towards Fuzzy Actuarial Credibility,” Proceeding of the Annual Meeting of the North American Fuzzy Information Processing Society, Allentown, Pennsylvania, August.
Lemaire, Jean, (1990) “Fuzzy Insurance,” ASTIN Bulletin, 20:33–56.
Myers, Stewart C. and Cohn, Richard A., (1987), “A Discounted Cash Flow Approach to Property-Liability Insurance Rate Regulations,” Chapter 3, 55–78 of J. D. Cummins and S. E. Harrington, editors, Fair Rate of Return in Property-Liability Insurance, Boston, Massachusetts, Kluwer-Nijhoff.
Myers, Stewart C., (1984), Paper prepared for the Massachusetts Automobile rate hearings, Massachusetts Rating Bureau Filing for 1985 Automobile Rates, Boston, Mass., December.
Ostaszewski, Krzysztof M., (1998), “Is Paul v. Virginia Dead?”, Fair Value of Insurance Liabilities, I.T. Vanderhoof and E. Altman, editors, Kluwer Academic Press, Boston, 351–360
Ostaszewski, Krzysztof M., (1993), An Investigation into the Possible Applications of Fuzzy Sets Methods in Actuarial Science, Society of Actuaries, Schaumburg, Illinois.
Panjer, H.H., and Bellhouse, D.R., (1980), “Stochastic modelling of interest rates with applications to life contingencies,” Journal of Risk and Insurance, 47:91–110.
Sametz, Arnold W., (1987), “The ‘New’ Financial Environment of the United States”, in Handbook of Financial Markets and Institutions, edited by Edward I. Altman, 6th edition, John Wiley and Sons, New York.
Trowbridge, C.L., (1989), Fundamental Concepts of Actuarial Science, Actuarial Education and Research Fund, Schaumburg, Illinois.
Tullis, Mark A., Polkinghorn, Philip K., (1992), Valuation of Life Insurance Liabilities, Second Edition, Actex Publications, Winsted, Connecticut.
Wong, F.S., Wang, P.Z., Goh, T.H., and Quek, B.K., (1992), “Fuzzy Neural Systems for Stock Selection,” Financial Analysts Journal, January/February, 48(1):47–52.
Young, Virginia R., (1996), “Insurance Rate Changing: A Fuzzy Logic Approach”, Journal of Risk and Insurance, 63:461–484.
Young, Virginia R., (1994), “The Application of Fuzzy Sets to Group Health Underwriting,” Transactions of the Society of Actuaries 45:551–584.
Zimmermann, H.J., (1991), Fuzzy Set Theory and its Applications, Second Edition, Kluwer Academic Publishers, Boston, Massachusetts.
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Derrig, R.A., Ostaszewski, K.M. (1999). Fuzzy Sets Methodologies in Actuarial Science. In: Zimmermann, HJ. (eds) Practical Applications of Fuzzy Technologies. The Handbooks of Fuzzy Sets Series, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4601-6_16
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DOI: https://doi.org/10.1007/978-1-4615-4601-6_16
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