MAS-I key terms

The tendency for individuals with higher-than-average expected losses to seek out or retain more insurance at a given price, because they know their own risk better than the insurer does.

The tendency for insureds to take fewer precautions, or to behave in riskier ways, because insurance softens the financial consequence of a loss.

The portion of each covered loss that the insured must pay before the insurer's payment begins, reducing the number and size of small claims and sharing risk.

A cost-sharing provision in which the insured and insurer split a covered loss in fixed percentages, typically applied to amounts above any deductible.

The maximum amount an insurer will pay under a policy, either per claim, per occurrence, or in total, capping the insurer's liability.

A transaction in which an insurer transfers part of its risk to another insurer in exchange for a share of premium, protecting against large or numerous claims.

The process of assessing an applicant's risk characteristics, then deciding whether to insure, at what price, and with what terms and conditions.

An insurer's estimate of the unpaid obligations for claims that have already occurred, including reported claims not yet settled and incurred but not reported claims.

For a nonnegative integer-valued random variable, the expected value of z raised to the random variable; its derivatives at z equal to one yield factorial moments.

The expected value of e raised to t times a random variable; derivatives at zero give the moments and, when finite near zero, it identifies the distribution.

The result that sums or averages of many independent, identically distributed variables with finite variance become approximately normal after standardization, regardless of the underlying distribution.

The parameter value that maximizes the likelihood function, the probability of the observed data treated as a function of the parameter; it is consistent and asymptotically efficient.

An estimation technique that equates sample moments to theoretical moments written in terms of unknown parameters, then solves the resulting equations for estimates.

A data-based interval constructed so that, over repeated samples, it contains the true parameter with a stated probability called the confidence level.

A formal procedure that uses sample evidence to decide between a null hypothesis and an alternative, with the significance level controlling the probability of a false rejection.

A counting process whose counts in disjoint time intervals are independent and Poisson, with a mean proportional to interval length, and whose increments are stationary.

A count distribution on nonnegative integers that is a Poisson mixture with a gamma-distributed mean, producing variance larger than the mean and longer tails.

A right-skewed distribution for a positive variable whose logarithm follows a normal distribution, often used to model claim severity and other positive losses.

An estimator whose expected value equals the true parameter value for every possible parameter, meaning its average over repeated samples hits the target.

The current worth of a future payment or stream of payments, obtained by applying a discount factor to reflect the time value of money.

The instantaneous rate at which a fund grows, equal to the derivative with respect to time of the logarithm of the accumulation function.

The single annual compound rate that produces the same year-end accumulation as the actual compounding arrangement, whatever nominal rate and compounding frequency are quoted.

A level payment stream made at the end of each period for a fixed number of periods, valued one period before the first payment occurs.

A level payment stream made at the start of each period; each payment arrives one period earlier, so its value exceeds the annuity-immediate value by a factor of one plus the rate.

The sum of present values of cash inflows minus outflows at a chosen interest rate; a positive value indicates a project adds value at that rate.

The present-value-weighted average of the times at which cash flows occur, used as a measure of a portfolio's sensitivity to interest rate changes.

A portfolio strategy that matches the duration and present value of assets and liabilities so that small parallel interest rate shifts leave surplus roughly unchanged.

A model of total losses in which claim counts and individual claim amounts are modeled separately, and the total is the random sum of severities.

A collective risk model whose claim count is Poisson and whose severities are independent, identically distributed, and independent of the claim count.

The random total of claim payments from a group of policies over a period, obtained by compounding a frequency distribution with a severity distribution.

A recursive algorithm that computes the distribution of aggregate losses when the claim count lies in the (a,b,0) class and severities are discretized onto a lattice.

A premium-setting method that blends a risk's own loss experience with a broader group's experience, weighting its own data according to volume and stability.

A credibility model in which the weight on own experience is the expected process variance divided by that variance plus the variance of hypothetical means.

The probability that an insurer's surplus, starting from initial capital and evolving with premiums and random claims, ever drops below zero.

The positive root of the Lundberg equation in the classical risk model, governing the exponential rate at which bounds on ruin probability decrease with starting capital.

The expected value of a loss capped at a chosen limit, written as the expected value of the minimum of the loss and the limit; used to value deductibles and limits.

A regression model in which the response distribution belongs to an exponential family and the mean is connected to a linear predictor through a link function.

Variability in count data that exceeds the variance assumed under a Poisson model, often handled by negative binomial or random-effects specifications.