Читать книгу Pricing Insurance Risk - Stephen J. Mildenhall - Страница 36

Every day, we take action, sometimes without being sure of the outcome. Some actions result from decisions we make, while others are inescapable. Some uncertain outcomes are well-defined such as with a lottery ticket or card game, but most are ill-defined: What kind of career would I have with a bachelor’s degree in statistics? What will my retirement be like with this amount of savings? Some are purely monetary, others related to health, family, politics, or world events. Bernstein (1996) summarizes how the modern world emerged, in part, because we developed better ways to understand and decide between actions with uncertain outcomes.

Our risk preferences have economically meaningful consequences. A decision depends on the riskiness of the outcome and the risk attitude of the decision maker (Diamond and Stiglitz 1973). When we act on our own behalf we are free to choose how to act; when we act as an agent we are required to act in a manner consistent with certain standards of behavior. There is substantial interest in decision theory: making consistent and considered choices between alternative courses of action with uncertain outcomes. Decision theory is a fundamental part of economics, finance, management, risk theory, and actuarial science.

Quantitative decision theory relies on numerical risk measures. A risk-based capital formula and an insurance pricing model are two examples of numerical risk measures. The definition, specification, and classification of risk measures is a central problem of actuarial science, with a long history (Borch 1962; Bühlmann 1970; Goovaerts, De Vylder and Haezendonck 1984).