Insurance: Mathematics and Economics 26 2000 119–132
A Hitchhiker’s guide to the techniques of adaptive nonlinear models
Arnold F. Shapiro
∗
Smeal College of Business, Penn State University, University Park, PA 16802, USA Received 1 December 1998; received in revised form 1 November 1999; accepted 24 November 1999
Abstract
Adaptive nonlinear models ANMs are currently being proposed for use in actuarial and financial modeling. The techniques of these models included such things as neural networks and genetic algorithms. While there is a general awareness of the
nature of these ANM techniques, there is often only vague familiarity with the details of how these techniques are implemented. This article is intended to help alleviate this situation. Its purpose is to present an overview of ANM techniques, which includes
an explanation of what they are, how they work, and a description of their key features. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Adaptive; Nonlinear; Techniques; Heuristic
1. Introduction
Adaptive nonlinear models ANMs are models of problems where there are important nonlinearities be-
tween the observables independent variables and the dependent variable, and, because the underlying the-
ory is not known, the situation dictates the use of an adaptive approach based on the observed data. ANM
techniques are the techniques upon which these mod- els are built.
Risk and insurance researchers generally have an awareness of the nature of ANM techniques. Most
know, e.g., that genetic algorithms are based on genet- ics and evolution, neural networks are based on how
the brain functions, chaos theory is related to the flap- ping of the wings of a butterfly, and some are even
aware that simulated annealing is based on thermody- namics. However, there is often only vague familiarity
∗
Tel.: +1-814-865-3961 E-mail address: afslemail.psu.edu A.F. Shapiro
with the details of how these techniques are imple- mented.
This dichotomy is unfortunate. Many researchers are confronted with problems where ANM techniques
are appropriate. These include problems that require a heuristic solution because of the vagueness of the
underlying theory, and situations involving nonlinear- ities, where there is an emphasis on not making un-
justified assumptions about the nature of those nonlin- earities. Since ANM techniques have the capacity to
overcome these issues, one would expect to see them implemented more often.
A plausible explanation of why ANM techniques are not being implemented more often is that po-
tential users are not sufficiently familiar with their characteristics and, consequently, forego opportuni-
ties for implementation. Assuming this to be the case, the purpose of this article is to help alleviate this
situation by presenting an overview of ANM tech- niques, which includes an explanation of what they
are, how they work, and a description of their key features.
0167-668700 – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 6 6 8 7 9 9 0 0 0 5 8 - X
120 A.F. Shapiro Insurance: Mathematics and Economics 26 2000 119–132
Fig. 1. ANM techniques.
2. A synopsis of ANM techniques
