ASA key terms

The theorem states that the sum or average of many independent, identically distributed random variables tends toward a normal distribution as the sample size grows, provided the underlying variance is finite.

A maximum likelihood estimator chooses parameter values that maximize the probability or likelihood of the observed sample under an assumed probability model.

A confidence interval is a range of plausible values for an unknown parameter, constructed so that a stated proportion of repeated intervals would contain the true value under the model.

The p-value is the probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the value actually obtained.

Simple linear regression models the conditional mean of a continuous response as a straight-line function of one predictor, often estimating an intercept and slope by least squares.

Logistic regression models the probability of a binary outcome by applying a logistic function to a linear combination of predictors, with coefficients commonly estimated by maximum likelihood.

A generalized linear model links a response variable's mean to a linear predictor through a specified link function and assumes a distribution from the exponential family.

Credibility theory blends an individual insured's own experience with broader collateral data, assigning weights based on how much predictive reliability the individual data demonstrate.

The survival function gives the probability that a person or entity survives beyond a specified age or time, starting from a defined initial age and remaining nonincreasing.

The force of mortality is the instantaneous rate of mortality at a given age, equal to the negative derivative of the log survival function with respect to age.

A life table summarizes mortality and survival patterns by age, typically showing counts of survivors, deaths, and probabilities used to compute insurance and annuity values.

A net premium is the expected present value of future benefits divided by an annuity factor for premiums, excluding expenses and profit, under a specified insurance contract and basis.

A gross premium includes expected benefits, expenses, profit, and risk margins, and is the amount actually charged to policyholders under the contract.

An actuarial reserve is the funds an insurer holds to meet future policy obligations, typically computed as the expected present value of future benefits minus future net premiums.

Thiele's differential equation describes how a policy reserve changes over time, accounting for interest, premiums, benefits, and the probability of decrement during the policy term.

A multiple decrement model tracks several ways a person can leave a population, such as death or withdrawal, using dependent probabilities and cause-specific decrement rates.

A Markov chain is a sequence of states where the probability of the next state depends only on the current state and not on the earlier history.

A Poisson process counts events occurring randomly over time so that counts in disjoint intervals are independent and the number in an interval has a Poisson distribution with rate proportional to length.

A compound Poisson distribution models a random total formed by summing a Poisson-distributed number of individual loss amounts, often used for aggregate insurance claims.

An aggregate loss model combines frequency and severity distributions to describe the total cost of many claims over a period, commonly through compound distributions.

Ruin probability is the chance that an insurer's surplus falls below zero at some time, given initial capital, premium income, and a model for claim arrivals and amounts.

Present value is the current worth of a future cash flow or series of cash flows, found by discounting each payment at an appropriate interest rate for its timing.

Accumulated value is the future worth of an investment or cash flow after interest has been credited, often computed by multiplying each payment by an accumulation factor.

The effective annual rate is the actual yearly growth rate implied by a nominal rate and compounding frequency, making different compounding conventions comparable on a one-year basis.

An annuity-immediate pays a level amount at the end of each period for a fixed number of periods; its present value is the sum of discounted payments.

The yield rate is the interest rate that equates the present value of all cash inflows to the present value of all cash outflows in an investment transaction.

Duration measures the sensitivity of a bond or cash-flow stream's present value to changes in interest rates, often expressed as a weighted average timing of cash flows.

Immunization is an asset-liability management strategy that selects assets so the portfolio's value remains sufficient for liabilities despite small changes in interest rates.

The no-arbitrage principle states that two portfolios producing identical future cash flows in every state should have the same current price, preventing riskless profit without investment.

Put-call parity is an arbitrage relationship linking European call and put prices with the same strike and expiry, the underlying asset price, and the present value of the strike.

The Black-Scholes formula prices European options on a non-dividend-paying stock using assumptions of continuous trading, constant volatility, and lognormally distributed stock prices.

Opportunity cost is the value of the next best alternative forgone when a resource is used for one purpose instead of another, measured in terms of benefits given up.

An income statement reports revenues, expenses, and profit or loss over an accounting period, showing how a business's operations translate into net income.

The bias-variance tradeoff describes how model error can be split into bias, variance, and irreducible noise, with more flexible models usually lowering bias but raising variance.

Cross-validation estimates out-of-sample performance by repeatedly splitting data into training and validation folds, fitting the model on training data, and scoring it on held-out data.

Regularization adds a penalty to a model's objective function to discourage excessive complexity, often shrinking coefficients toward zero and improving predictive performance on new data.

Stationarity means a time series has statistical properties such as mean, variance, and autocorrelation that do not change over time, simplifying model estimation and forecasting.

An autoregressive model predicts a time series value using a linear combination of its own past values plus an error term, capturing short-term dependence.

The actuarial present value is the expected present value of future contingent cash flows, weighting each possible payment by both interest discounting and the probability of payment.