Key Terms

Black swan: a rare event with catastrophic consequences, which is impossible to predict using standard analytical tools and historical data.

Continuous random variable: A random variable whose outcome can take on any real value in an interval.

Discrete random variable: A random variable whose outcomes are countable.

Downside risk: The risk associated with a potential loss, damages, or injury. Sometimes used to refer specifically to the risk of extreme losses.

Ex ante: Translates to “before the event,” our expectations of an event before it has occurred.

Exhaustive: Events are (collectively) exhaustive if together they cover all possible outcomes of a random experiment. For example, a coin must either land on “heads” or “tails,” there is no other possible outcome, and so these events are exhaustive.

Expected shortfall: The average of the worst possible cases measured at a given Value-at-Risk (VaR).

Expected value: See mean

Ex post: Translates to “after the event,” our knowledge of an event once it has occurred.

Frequency distribution: A graph or table that displays how often various outcomes occurred.

Indemnify: When an insurance claim is made, the insurance company indemnifies (compensates) the insured for their losses.

Kurtosis: Kurtosis captures information about the probability of obtaining extreme positive and negative values relative to normal distribution.

Law of large numbers: A theorem that states that the sample mean tends towards the true mean with a sufficiently large number of independent samples. For example, if we flip a fair coin only a hundred times, we may happen to land on “heads” in most trials. However, if we flip the coin several hundred times, we know with high confidence about half will be heads.

Mean: The mean of a random variable is the probability-weighted average of all possible outcomes. Also called the expected value of a random variable.

Mutually exclusive: Events that are mutually exclusive are events that cannot happen at the same time. For example, a coin cannot land on both “heads” and “tails” during a single toss and so its outcomes are mutually exclusive.

Normal distribution: A common distribution for continuous random variables that is symmetric about the mean. In a normal distribution, about 68% of the outcomes lie within one standard deviation of the mean, 95% of outcomes within two standard deviations, and 99.7% of outcomes within 3 standard deviations of the mean.

Overconfidence: The human tendency to overestimate our actual ability to perform a task successfully.

Premia: The regular insurance payments made to an insurer in exchange for bearing risk.

Probability: The likelihood that an event will occur.

Random variable: A random variable is a function that assigns numerical values to all possible outcomes of an experiment (or other random process). For example, when tossing a fair coin, a random variable could assign the value 1 to the outcome “heads” and the value 0 to the outcome “tails.”

Risk: There are several definitions for risk; they typically refer to the notion that outcomes may be different than we predict or expect. In insurance, risk often refers specifically to the possibility of injury or other damages (see downside risk).

Skewness: A measure of asymmetry for a probability distribution. If a distribution is symmetric, it will have skewness equal to 0.

Standard deviation: A measure of how spread-out values are from their mean. The higher the standard deviation, the more variance there is in outcomes.

State of the world: A possible future scenario.

Subjective probability: The likelihood an individual attributes to an event based on the individual’s own experience or personal judgment.

Value-at-Risk (VaR): A measure of downside risk commonly used by banks, insurers, and investment companies.