Patrick L. Brockett

Using Kohonen's Self-Organizing Feature Map to Uncover Automobile Bodily Injury Claims Fraud

Claims fraud is an increasingly vexing problem confronting the insurance industry. In this empirical study, we apply Kohonens Self-Organizing Feature Map to classify automobile bodily injury (BI) claims by the degree of fraud suspicion. Feed forward neural networks and a back propagation algorithm are used to investigate the validity of the Feature Map approach. Comparative experiments illustrate the potential usefulness of the proposed methodology. We show that this technique performs better than both an insurance adjusters fraud assessment and an insurance investigators fraud assessment with respect to consistency and reliability.

Data transformations in DEA cone ratio envelopment approaches for monitoring bank performances

Abstract Cone ratio DEA (Data Envelopment Analysis) models are suggested for monitoring and/or early warning systems to be used by bank regulatory agencies. Illustrative examples are developed from data on 1984 and 1985 performances of the 16 largest banks in Texas. Five large non-Texas banks are introduced as “excellent performers” to help evaluate these Texas banks in terms of their “risk coverage” as well as “efficiency”. Cone ratio envelopment areused to tarnsform original data in order to reflect performances by the non-Texas banks with respect to “risk coverage” as well as “efficiency”. Formulas for transforming to and from the original data are supplied with accompanying explanations and interpretations which include comparisons with the “risk-adjusted capital” and “risk-coverage” allowances formulas that have been adopted recently by U.S. Government (and other) regulators in banking (and insurance) in conformance with the “Basel Agreement” of 1988.

Nonlinear and non‐Gaussian ocean noise

Bispectral analysis is a statistical tool for detecting and identifying a nonlinear stochastic signal generating mechanism from data containing its output. Bispectral analysis can also be employed to investigate whether the observed data record is consistent with the hypothesis that the underlying stochastic process has Gaussian distribution. From estimates of bispectra of several records of ambient acoustic ocean noise, a newly developed statistical method for testing whether the noise had a Gaussian distribution, and whether it contains evidence of nonlinearity in the underlying mechanisms generating the observed noise is applied. Seven acoustic records from three environments are examined: the Atlantic south of Bermuda, the northeast Pacific, and the Indian Ocean. The collection of time series represents both ambient acoustic noise (no local shipping) and noise dominated by local shipping. The three ambient records appeared to be both linear and Gaussian processes when examined over a period on the ord...

Inefficiency and congestion in Chinese production before and after the 1978 economic reforms

Abstract Congestion is identified with input increments that result in output decrements. A new model in DEA (Data Envelopment Analysis) developed for identifying congesting inputs and estimating their impact is here applied to Chinese data over the period 1966–1988 for 3 industries: Textiles (labour intensive), Chemicals (capital intensive) and Metallurgical (in between these two extremes)—to identify sources and estimate amounts—where this model is used. Congestion is identified as occurring only in labour and primarily in years preceding the 1978 economic reforms. Chinas large labour employment problem and associated worker welfare programs suggest that some tradeoff with output reductions may have been desired in these periods. However, it is also shown how these DEA congestion models can be used to identify tradeoffs that could have been used to improve either, or both, output and labour employment. Although restricted to identifying possibilities for augmenting employment in the present paper, this approach can also be used in DEA applications where other types of input as well as output augmentations are desirable. Appendix A compares the approach in this paper with previously available approaches to congestion.

A generalized data envelopment analysis model: A unification and extension of existing methods for efficiency analysis of decision making units

In this paper, we introduce a generalized Data Envelopment Analysis (DEA) model which unifies and extends most of the well-known DEA models developed over the past fifteen years and points the way to new models. By setting three binary parameters of this model to different values, we obtain subclasses of the DEA models with generalK cone andW cone descriptions to represent the evaluators preferences for the Decision Making Units (DMU) and the input/output categories. We also show relationships among the various different subclasses of the generalized DEA model and give special attention to efficiency definitions and solutions. Furthermore, we state and rigorously prove the equivalence between DEA efficiency and the nondominated solutions of a corresponding multi-objective program. This latter result is especially important for understanding and interpreting the concept of efficiency. Detailed examples are also presented to demonstrate the functions ofK cone andW cone, as well as their characteristics.

WEATHER DERIVATIVES AND WEATHER RISK MANAGEMENT

Weather derivatives are a relatively recent kind of financial product developed to manage weather risks, and currently the weather derivatives market is the fastest-growing derivative market. The development of weather derivatives represents one of the recent trends toward the convergence of insurance and finance. This article presents an overview of weather risks, weather derivatives, and the weather derivatives market, and examines the valuation of weather derivatives in an incomplete market, the hedging effectiveness of standardized weather derivatives, as well as optimal weather hedging with the consideration of basis risk and credit risk.

Evaluating solvency versus efficiency performance and different forms of organization and marketing in US property--liability insurance companies

Abstract Solvency is a primary concern for regulators of insurance companies, claims paying ability is a primary concern for policyholders, and return on investment is a primary concern for investors. These interests potentially conflict, and the decision-makers for the firm must trade off one concern versus another. Here we examine the efficiency of insurance companies via data envelopment analysis using solvency, claims paying ability, and return on investment as outputs and using a financial intermediary model for the insurance company. The effect of solvency on efficiency is then examined. These efficiency evaluations are further examined to study stock versus mutual form of organizational structure and agency versus direct marketing arrangements, which are examined separately and in combination.

Bispectral-Based Tests for the Detection of Gaussianity and Linearity in Time Series

Abstract Statistical techniques have been developed that use estimated bispectrum values to test whether a sample of a time series is consistent with the hypothesis that the observations are generated by a linear process. The magnitude of the test statistics indicates the amount of divergence between the observations and the linear model hypothesis. It is important to investigate such a divergence, since the usual linear model coefficients can be shown to be biased in the face of nonlinear time series structure. The tests presented here can thus be considered diagnostic as well as confirmatory. These tests are applied to a variety of real series previously modeled with linear models. The results indicate nonlinear models may yield better results, because many of the series analyzed appear to have considerable nonlinear lagged interactions.

Construction of all DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis Model

Abstract In this paper, we study the structural properties of DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis (GDEA) model introduced by Yu, Wei and Brockett (1996). The GDEA model contains the following well-known Data Envelopment Analysis (DEA) models as its special cases: the CCR model by Charnes, Cooper, and Rhodes (1978); the BCC model by Banker, Charnes and Cooper (1984); The FG model by Fare and Grosskopf (1985); and the ST model by Seiford and Thrall (1990). The relationships among Decision Making Units (DMUs) can be found by solving the GDEA model with predilection cone description. Using these relations to identify relative positions of the DMUs on the DEA efficient surface, we devise an efficient algorithm for constructing all the DEA efficient surfaces. Through further analysis, we show properties of DEA-efficient surfaces under several important subclasses of DEA models. Analytical expressions for the DEA efficient surfaces are obtained, which are useful in analyzing the structure of DEA efficiencies and in strategic group classifications. Results from this paper suggest important applications in constructing Pareto solutions (or nondominated solutions) and in analyzing structural properties of Pareto solutions in multiobjective programming.

A Reexamination of the Relationship Between Preferences and Moment Orderings by Rational Risk-Averse Investors

This article examines the relationship between risk, return, skewness, and utility-based preferences. Examples are constructed showing that, for any commonly used utility function, it is possible to have two continuous unimodal random variables X and Y with positive and equal means, X having a larger variance and lower positive skewness than Y, and yet X has larger expected utility than Y, contrary to persistent folklore concerning U‴ > 0 implying skewness preference for risk averters. In additon, it is shown that ceteris paribus analysis of preferences and moments, as occasionally used in the literature, is impossible since equality of higher-order central moments implies the total equality of the distributions involved.