Risk Measurement and Insurance Pricing Vocabulary

A set of vocabulary flashcards defining primary terms, mathematical relationships, and premium components from the lecture notes on risk measurement and evaluation.

Risk

Uncertainty or variation around the expected loss, representing the difference between expected loss and actual loss.

Statistical Probability

The practice of using past data or historical observations to estimate the likelihood of an event occurring in the future.

Loss Frequency

A measure of how often a loss occurs ($E(F)$) over a given exposure period.

Loss Severity

The dollar ($) amount or financial magnitude of a loss when it occurs ($E(S)$$).

Expected Loss ($EL$)

The total anticipated monetary loss per exposure over a specified time period, calculated as $EL = E(F) \times E(S)$.

Law of Large Numbers

A foundational statistical rule stating that as the number of exposure units or observations increases, actual loss outcomes converge closer to the expected loss outcome.

Random Variable

A variable whose resulting numerical value depends on a chance event or random outcome.

Objective Risk

The relative variation of actual losses from expected losses, quantifying how much actual results can deviate from predicted outcomes ($\frac{AL - EL}{EL}$).

Gross Premium

The total amount paid per unit of coverage to insure a specific risk, structured as $\text{Gross Premium} = \text{Pure Premium} + \text{Risk Charge} + \text{Administrative Costs}$.

Pure Premium

The portion of the gross premium calculated to be sufficient to cover expected losses only, defined as $\text{Pure Premium} = \text{Expected Loss}$.

Risk Charge

An extra fee added to the gross premium that compensates the insurer for estimation risk and uncertainty regarding expected losses.

Administrative Costs (Expense Loading)

The operating expenses of running an insurance enterprise (such as employee wages, marketing, advertising, claims processing, and state premium taxes), typically comprising $20\%$ to $40\%$ of the gross premium.

Estimation Risk

The uncertainty an insurer faces because future actual losses may deviate from historical loss estimates.

State Premium Tax

A tax levied by state governments on insurance premiums collected by insurers (typically $2\%$ to $5\%$), which is built directly into administrative expense loadings paid by policyholders.

Mean (Expected Outcome)

A measure of central tendency representing the weighted average or expected result across a dataset.

Variance

A statistical measure of dispersion evaluating how spread out actual loss outcomes are around the mean.

Standard Deviation ($SD$)

The square root of variance, serving as a direct quantitative measure of risk and variability around expected outcomes.

Coefficient of Variation ($COV$)

A normalized metric of relative risk calculated as $\text{COV} = \frac{\text{SD}}{\text{Mean}}$, where a higher $\text{COV}$ indicates greater variability relative to expected loss.

Maximum Possible Loss

The absolute worst-case financial loss that could theoretically occur to an exposure unit, regardless of probability.

Maximum Probable Loss

The largest financial loss that is reasonably likely to occur given a specified level of probability or confidence.

Surplus Lines Market

An unregulated insurance marketplace (such as Lloyd's of London) utilized for insuring high-risk, unique, non-standard, or unusual exposures.