290 A.F. Shapiro, R. Paul Gorman Insurance: Mathematics and Economics 26 2000 289–307
Fig. 1. ANM technologies.
ing signals Brockett et al., 1994, credit card risk and profitability, where the focus has been on the
modeling of response characteristics, profitability and fraud Gorman, 1996, and claim fraud in bodily in-
jury claims Brockett et al., 1998.
The purpose of this paper is to discuss, in concep- tual rather than technical terms, the issues related to
the implementation of ANMs. The topics covered in- clude: a short overview of ANM technologies; mod-
eling considerations; the model development process; and a comparison of linear and nonlinear models.
2. The underlying technologies
Adaptive nonlinear modeling involves the develop- ment of crafted solutions driven by the nature of the
modeling problem and requires the integration of com- plimentary technologies. The diversity of these ANM
technologies is depicted in Fig. 1,
3
and briefly de- scribed in the statement that follows:
• Evolutionary optimization EV is an approach to
the design of learning algorithms that is structured along the lines of the theory of evolution. While EV
includes GAs, genetic programming, and evolution strategies, the primary focus in this paper is GAs.
• Fuzzy logic FL is a superset of conventional logic
extended to handle the concept of partial truths. •
Intelligent agents are software applications that au- tomate tasks. They recognize events and use do-
main knowledge to take appropriate actions based on those events.
3
A simple overview of many of these technologies is found in Shapiro, 2000.
• Expert systems are designed to replicate the
problem-solving capability associated with a spe- cialized domain human expert.
• Bayesian belief networks are systems that rep-
resents cause and effect relationships among vari- ables, along with probabilities that each cause vari-
able will influence each effect variable. It is an alter- native to fuzzy expert systems for combining expert
knowledge with inferences derived from historical data.
• Case-based reasoning is an approach to problem
solving based on the retrieval and adaptation of cases.
• Rule induction induces logical rules from historical
data and then applies the rules to make predictions on other given data.
• Learning vector quantization LVQ Kohonen,
1988, Section 7.5 is a neural computing paradigm used to improve the classification accuracy in pat-
tern recognition problems.
• Statistical inference is the process of drawing in-
ferences from functions on samples statistics to functions on populations parameters.
• Neural-fuzzy systems are combinations of NNs with
expert fuzzy systems. •
NNs are nonlinear predictive models that learn both structure and parameter values through training,
which also superficially resemble biological NNs in structure.
• Operations research OR, from a methodology ori-
entation, is the application of quantitative methods to solve practical problems.
4
Some of these technologies, like OR and statistical inference, are well-known. Others, while of somewhat
more recent vintage, are relatively common. These in- clude expert systems, Bayesian belief networks, in-
telligent agents, case-based reasoning, and rule induc- tion. Still others, like the soft computing technolo-
gies
5
EV, NNs, FL, and hybrids of these, have only recently been added to the actuary’s arsenal. The next
section provides a brief introduction to the soft com- puting technologies, and is intended for those read-
4
Some would regard this methodology oriented view of OR as too narrow. Jewell 1980, p. 113, for example, would prefer to
stress the system building opportunities and areas for constructive interaction, rather than the tools and techniques of OR.
5
Soft computing is a concept that was introduced by Zadeh 1992, the discoverer of FL.
A.F. Shapiro, R. Paul Gorman Insurance: Mathematics and Economics 26 2000 289–307 291
ers who are unfamiliar with the area. Following that, the reminder of this section discusses the grouping
of ANM technologies into functional classes and the team approach.
3. The soft computing technologies
