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Fuzzy Financial Pricing of Property-Liability Insurance

Author

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  • J. David Cummins
  • Richard Derrig

Abstract

This paper uses fuzzy set theory (FST) to solve a problem in actuarial science, the financial pricing of property-liability insurance contracts. The fundamental concept of FST is the alternative formalization of membership in a set to include the degree or strength of membership. FST provides consistent mathematical rules for incorporating vague, subjective, or judgmental information into complex decision processes. It is potentially important in insurance pricing because much of the information about cash flows, future economic conditions, risk premiums, and other factors affecting the pricing decision is subjective and thus difficult to quantify by using conventional methods. To illustrate the use of FST, we “fuzzify” a well-known insurance financial pricing model, provide numerical examples of fuzzy pricing, and propose rules for project decision-making using FST. The results indicate that FST can lead to significantly different decisions than the conventional approach.

Suggested Citation

  • J. David Cummins & Richard Derrig, 1997. "Fuzzy Financial Pricing of Property-Liability Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(4), pages 21-40.
    • Handle: RePEc:taf:uaajxx:v:1:y:1997:i:4:p:21-40
    DOI: 10.1080/10920277.1997.10595640
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    Cited by:

    1. Lai, Li-Hua, 2008. "An evaluation of fuzzy transportation underwriting systematic risk," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(9), pages 1231-1237, November.
    2. Jorge De Andrés Sánchez & Antonio Terceño Gómez, 2003. "Applications of Fuzzy Regression in Actuarial Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 665-699, December.
    3. Ali Azadeh & Mohammad Sheikhalishahi & Ali Boostani, 2014. "A Flexible Neuro-Fuzzy Approach for Improvement of Seasonal Housing Price Estimation in Uncertain and Non-Linear Environments," South African Journal of Economics, Economic Society of South Africa, vol. 82(4), pages 567-582, December.
    4. de Andres-Sanchez, Jorge, 2007. "Claim reserving with fuzzy regression and Taylor's geometric separation method," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 145-163, January.
    5. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
    6. Shapiro, Arnold F., 2002. "The merging of neural networks, fuzzy logic, and genetic algorithms," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 115-131, August.
    7. Jorge De Andrés-Sánchez, 2024. "Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method," Mathematics, MDPI, vol. 12(6), pages 1-24, March.
    8. Liu, Ying & Li, Xiaozhong & Liu, Yinli, 2015. "The bounds of premium and optimality of stop loss insurance under uncertain random environments," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 273-278.
    9. Shapiro, Arnold F. & Paul Gorman, R., 2000. "Implementing adaptive nonlinear models," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 289-307, May.

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