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...contract. that auditing becomes more effective and overcompensation can be reduced, when insurers are able to condition their audits on the information provided by detection systems.
INTRODUCTION
Fraud is a well-known phenomenon in insurance markets, since policyholders usually have private information about the occurrence of an insured loss. The Costly State Verification approach (Townsend, 1979) concentrates on fraud situations where the principal is able to verify reports of the agent through costly audits. Consequently, the model focuses on two incentive devices: explicit contracts and costly audits. The range of economic applications is manifold. For instance, Gale and Hellwig (1985) consider credit relationships, whereas Mookherjee and Png (1989) refer to taxation problems.
Since the above-mentioned papers regard auditing problems with commitment, the revelation principle (1) applies, and therefore, the agent truthfully reports his private information. As a consequence, insurance fraud can be prevented entirely. However, in many situations the principal is not able to credibly commit herself ex ante to an audit strategy. Although some papers, as for example, Melumad and Mookherjee (1989) or Picard (1996), propose solutions for the noncommitment problem, these approaches are not universally applicable. Consequently, the insurer's inability to credibly commit herself causes an inevitable market inefficiency, because policyholders will have an incentive to make fraudulent reports, as Picard (1996) and Boyer (2000) show. In such a situation the contract between the principal and the agent can partly serve as a strategic incentive device. More precisely, the overcompensation of agents is the only possibility to limit fraud, as was previously shown by Khalil (1997) and Boyer (1999).
This article concentrates on the impact of fraud detection systems on the auditing procedure of insurers and on the overcompensation of policyholders. Although some papers, like Belhadji, Dionne, and Tarkhani (2000) and Artis, Ayuso, and Guillen (2002), analyzed fraud detection methods, to the best of our knowledge only Dionne, Giuliano, and Picard (2003) look at an auditing model with fraud detection. This is surprising, because detection systems are very popular and effective in existing insurance markets. For instance, in Germany a reinsurer and a software provider have jointly developed various detection systems, in cooperation with more than ten primary insurers, for different lines of insurance, like property, liability, and auto insurance. Due to the system, the know-how of fraud experts can be duplicated and suspicious claims can be identified more easily. Furthermore, an insurer can concentrate on more suspicious claims and can therefore improve the effectiveness of its audits. (2) First of all, these lines, in which detection systems are used, are evidently susceptible to insurance fraud. But, more importantly, they usually contain a considerable number of policyholders. As we show, the market size or, more precisely, the number of policyholders are crucial for the use of a detection system that causes significant fixed cost. (3) In this article, we consider a fraud detection system which provides soft information about the true state of the world. This information is modeled similar to Holmstrom (1979) as an additional signal that cannot be intentionally manipulated by the policyholder. (4)
Our main goal is to analyze the following problems: Which effects does a detection system have on the auditing game and the underlying insurance contract? And how can a detection system with fixed cost be implemented in a competitive insurance market without any market intervention? As the first proposition indicates, an informative system leads, ceteris paribus, to a lower fraud and audit probability, which is quite intuitive. As a further consequence, the overcompensation of agents can be reduced after the implementation of an informative detection system, because auditing becomes more effective. The welfare gains due to a system depend on the quality of the signal. Finally, we explore conditions under which a fraud detection system will be applied in a competitive insurance market. Extending the work by Picard (1996) and Boyer (2000), we give a new motivation for the use of an external party, such as a private supplier or an Insurance Fraud Bureau. The important role of the third party in our model is to transform the prevailing fixed implementation cost of a fraud detection system, which can lead to a market breakdown, if firms compete in prices la Bertrand, into variable cost.
The remainder of the article is organized as follows. In the next section, some important results of Boyer (2000) are briefly summarized. His model represents the reference case without fraud detection. The section "Equilibrium With Fraud Detection" concentrates on the effects of a fraud detection system on the equilibrium of the audit game and the underlying insurance contract. Furthermore, in the section "The Organizational Design of Fraud Detection" we derive conditions under which a system will be implemented, and show how the fraud detection process should be organized. We conclude the analysis in the section "Conclusions" with some final remarks and a brief outlook.
EQUILIBRIUM WITHOUT FRAUD DETECTION
The following framework is assumed. There are N homogenous and risk-averse agents (policyholders) with the same attitude toward insurance frauds and the same initial income Y > 0. Each policyholder possesses a continuous and twice differentiable utility function u(W) of final wealth W, with u'(W) > 0, u"(W) 0. It is assumed that the loss is not higher than the policyholder's initial income L < Y, and that insured policyholders have private information about the state of the world.
Additionally, we assume an insurance market with free entry and I [greater than or equal to] 2 risk-neutral principals (insurance companies), which offer insurance contracts C simultaneously. A contract consists of an insurance premium [alpha] [member of] [R.sup.+.sub.0] and an indemnity [beta] [member of] [R.sup.+.sub.0]. (6) In the Bertrand equilibrium, premium offers correspond to the expected marginal cost of a policyholder. Thus, in absence of any fixed cost, all insurance companies offer the same contract with a utility-maximizing indemnity at zero-expected profits and share the market equally.
The sequence of play is given in Figure 1.
[FIGURE 1 OMITTED]
After the policyholder has observed the state of nature, he decides whether to file a claim or not. Consequently, an insurance company has to decide whether to...
NOTE: All illustrations and photos
have been removed from this article.
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