As insurance companies hold portfolios of insurance policies that may result in claims, it is a good management practice to assess the exposure of the company to such risks. Arisk measure, which summarizes the overall risk exposures of the company, helps the company evaluate if there is sufficient capital to overcome adverse events. Risk measures for blocks of policies can also be used to assess the adequacy of the premium charged. Since the Basel Accords I and II, financial institutions such as banks and insurance companies have elevated their efforts to assess their internal risks as well as communicating the assessments to the public.

In this chapter we discuss various measures of risks. We introduce the axioms proposed by Artzner et al. (1999), which define the concept of a coherent risk measure. Risk measures based on the premium principle, such as the expected-value principle, variance principle, and standard-deviation principle, are discussed. This is followed by the capital-based risk measures such as the Value-at-Risk and the conditional tail expectation. Many of the risk measures used in the actuarial literature can be viewed as the integral of a distortion function of the survival function of the loss variable, or the mean of the risk-adjusted loss. Further risk measures that come under this category are risk measures defined by the hazard transform and the Wang (2000) transform.