Fuzzy logic in insurance
Introduction
It has been 20 years since the first article on fuzzy logic (FL) in insurance (DeWit, 1982) appeared in volume 1 of this journal.1 That article sought to quantify the fuzziness in underwriting. Since then, the universe of discourse has expanded considerably and now includes FL applications involving classification, underwriting, projected liabilities, future and present values, pricing, asset allocations and cash flows, and investments.
This article presents an overview of these FL applications in insurance. The specific purposes of the article are two-fold: first, to review FL applications in insurance so as to document the unique characteristics of insurance as an application area; and second, to document the extent to which FL technologies have been employed.
The structure of this article is as follows. The next section presents a review of the conceptual aspects of the fuzzy systems discussed in this article, and includes, at the end of the discussion of each methodology, a list of applications in the article that use that methodology. Following that is a chronological review of the insurance applications of FL by application area.2 This is done in two major sections: the first section of the review presents studies where FL is the only technology employed; the second section presents studies where the FL is used in conjunction with neural networks and/or genetic algorithms. The article ends with a comment on the future of FL in insurance.
Section snippets
Fuzzy logic methodology
In this article, we generally follow the lead of Zadeh (1965), the founder of FL, and use the term FL in its broad sense. According to Zadeh,3
Fuzzy logic, FL, has four principal facets. First, the logical facet, FL, the logic of approximate reasoning, which is fuzzy logic in its narrow sense. Second, the set-theoretic facet, FLs, which is concerned with classes having unsharp boundaries, that is, with fuzzy sets.
Applications involving only fuzzy logic
This section reports on the following insurance areas where FL has been implemented: classification, underwriting, projected liabilities, fuzzy future and present values, pricing, asset allocation, cash flows, and investments. Only studies that focus on FL are included in this section; studies that combine FL with neural networks and/or genetic algorithms are reviewed in Section 4. Also, some of the articles fit into more than one application category, and were arbitrarily assigned a category.
Soft computing applications
Most of the previously discussed studies focused on FL to the exclusion of other technologies. While their approach has been productive, it may have been sub-optimal, in the sense that studies may have been constrained by the limitations of FL, and opportunities may have been missed to take advantage of potential synergies afforded by other technologies.
This notion was embodied in the concept of soft computing (SC), which was introduced by Zadeh (1992).30
Conclusions
The purpose of this article has been to provide an overview of FL applications in insurance. As we have seen, FL has been applied in many insurance areas including classification, underwriting, projected liabilities, fuzzy future and present values, pricing, asset allocation, cash flows, and investments. By the same token, many of the FL techniques have been applied in the insurance area, including fuzzy arithmetic, fuzzy inference systems, and fuzzy clustering.
The overviews verify that FL has
Acknowledgments
This work was supported in part by the Robert G. Schwartz Faculty Fellowship and the Smeal Research Grants Program at the Penn State University. The assistance of Asheesh Choudhary, Bharath Nemali, Laura E. Campbell and Michelle L. Fultz is gratefully acknowledged.
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