Statistical and Financial Models of Insurance Pricing and the Insurance Firm

Statistical and Financial Models of Insurance Pricing and the Insurance Firm Although the field of risk and insurance is sometimes said to lack a central paradigm, several paradigms exist that define the foundations of the discipline. Two of the most important are: (1) the pure statistical model of insurance risk pools, which originates in probability theory and actuarial science; and (3) the financial model of the insurance firm and insurance pricing that draws upon modern financial theory. The two paradigms taken together constitute an important component of the core of the field of risk and insurance or insurance economics. Insurance demand theory and applications of various branches of economics such as industrial organization also are important elements of this core. To a significant extent the existing strands of insurance research have emerged in parallel, and few serious attempts at integration have been carried out. One reason for this is that each area is highly specialized and technical. Insurance-oriented textbooks that successfully bridge the gap between the specialist and a wider audience do not exist. In order for the field of risk and insurance to progress more rapidly, this obstacle must be overcome. The objective of this paper is to take an initial step in that direction by providing an introduction to the central results of two of the principal strands of insurance research: statistical and financial models of insurance pricing and the insurance firm. The next section considers statistical models. In spite of the critical importance of risk pooling in insurance, the statistical foundations of this phenomenon are not well-understood by many insurance experts. Misstatements and fallacies regarding pooling, laws of large numbers, the central limit theorem, and related concepts are pervasive, ranging from principles of insurance courses in the classroom to insurance tax cases in the federal courtroom. This problem exists even though the basic statistical concepts are relatively simple and can be understood and appreciated without a high level of mathematical training. Section I attempts to correct this problem by discussing the implications of the law of large numbers and central limit theorem for insurance risk pooling and by analyzing some of the more persistent insurer's risk fallacies. The discussion then turns to collective risk theory, which provides the most sophisticated statistical model of insurance. This field, which originated primarily in Europe, has experienced some recent advances that significantly increase its potential for practical application. A later section of the paper focuses on financial models of insurance. Financial modelling is one of the most rapidly growing fields of insurance research, particularly on the international scene. The paper provides an introduction to the basic financial applications in insurance. This discussion covers the insurance capital asset pricing model (CAPM), discounted cash flow modeling, and options modeling. Duration, immunization, and asset/liability management also are discussed. The emphasis throughout is on theoretical developments, but the reader should be aware that a growing empirical literature also exists, providing a possible topic for a future review article. Major progress in understanding insurance pricing and insurance markets can be achieved through the integration of the statistical and financial theories of insurance pricing and insurance firms. If this article provides the foundation of knowledge to assist researchers in beginning the integration process, it has accomplished its objective. Statistical Models of Insurance Individual Risk Theory The Model. A basic model that provides some important insights into the pooling process is individual risk theory (see Cummins (1974), Bowers, et al. (1986)). The random variable analyzed is the total monetary amount of claims arising from an insurance pool during a specified reporting period (e. …