PJENL Actuario Aptitude Exam key terms

A triple consisting of a sample space of outcomes, a collection of events closed under complement and countable union, and a probability measure assigning each event a number between 0 and 1 with total mass 1.

A measurable function mapping each outcome in a sample space to a real number, so that probabilities can be assigned to statements about its values.

The function giving, for each real number x, the probability that a random variable is less than or equal to x; it is nondecreasing, right-continuous, and tends to 0 and 1 at the extremes.

For a continuous random variable, a nonnegative function whose integral over an interval equals the probability the variable falls in that interval; it is the derivative of the distribution function where that exists.

The probability-weighted average of a random variable's possible values, computed as a sum in the discrete case or an integral in the continuous case; it is linear in the variable.

The expected squared deviation of a random variable from its mean, measuring dispersion; its square root is the standard deviation and it equals the second moment minus the square of the mean.

The expected product of the deviations of two random variables from their respective means; positive values indicate they tend to move together, and it is bilinear and symmetric.

Covariance of two variables divided by the product of their standard deviations, giving a dimensionless measure between minus one and one of linear association.

The probability an event occurs given that another event with positive probability has occurred, defined as the probability of both divided by the probability of the conditioning event.

A rule expressing a posterior conditional probability in terms of the likelihood and a prior probability, obtained by applying the definition of conditional probability twice.

The expected value of a random variable computed using a conditional distribution given known information; it is itself a random variable when the conditioning information is random.

An identity stating that the variance of a variable equals the expected conditional variance given a second variable plus the variance of its conditional expectation.

The expected value of the exponential of t times a random variable, viewed as a function of t; its derivatives at zero yield the moments when it exists near zero.

A result stating that standardized sums of many independent, identically distributed variables with finite variance converge in distribution to the standard normal distribution.

The parameter value that maximizes the likelihood function, the joint density of the observed sample treated as a function of the parameter; often found by maximizing the log-likelihood.

A random interval constructed from sample data so that, over repeated sampling, it covers the true parameter with a stated long-run probability called the confidence level.

A decision procedure that compares observed data with a null hypothesis using a test statistic, rejecting the null when the statistic falls in a prespecified rejection region.

The amount to which an initial investment grows after interest is credited over a period, equal to the principal multiplied by the accumulation function at that time.

The amount that, invested today at the given interest basis, would grow to a specified future amount; it is the future amount multiplied by the discount factor.

The ratio of interest earned during a period to the amount at the start of that period, measuring growth over one full period without compounding within it.

A quoted annual rate convertible m times per year, where each conversion applies the rate divided by m; it differs from the effective annual rate unless m equals one.

The instantaneous rate of growth of a fund per unit of time, equal to the derivative of the log accumulation function; for constant interest it equals the log of one plus the effective rate.

The present value of one unit payable one period from now, equal to one divided by one plus the effective interest rate; it converts future cash flows to present values.

A series of level payments made at the end of each period for a fixed number of periods; its present value is denoted by a-angle-n at the applicable interest rate.

A series of level payments made at the beginning of each period for a fixed number of periods; each payment is one period earlier than under an annuity-immediate, so its value is that of an annuity-immediate multiplied by one plus the interest rate.

The sum of the present values of all cash inflows minus outflows of a project at a given interest rate; a positive value suggests the project adds value at that rate.

The interest rate at which a project's net present value equals zero, provided such a rate exists and is unique for the cash flow pattern considered.

A present-value-weighted average of the times at which cash flows occur, used to approximate the sensitivity of a present value to small changes in the interest rate.

The probability that a person aged zero survives to at least age x, defined as one minus the distribution function of the age at death; it is nonincreasing in x.

The instantaneous rate of death at age x among those alive at that age, equal to the negative derivative of the log of the survival function.

A tabulation by age of quantities such as the number living, number dying, and death probabilities, typically starting from a radix of lives at age zero.

The expected present value of a future contingent payment stream, discounting each possible payment by both interest and the probability that it is made.

The level premium whose actuarial present value equals the actuarial present value of future benefits, computed without loading for expenses or profit.

The actuarial present value of future benefits minus the actuarial present value of future net premiums at a given duration, representing funds held for obligations already accrued.

A model in which aggregate claims over a period are the sum of a random number of individual claim amounts, with claim counts and amounts treated as independent.

The distribution of a random sum of independent, identically distributed claim amounts where the number of claims follows a Poisson distribution; its mean is the product of the count mean and the amount mean.

A method of setting a risk's rate by taking a weighted average of the risk's own experience and a broader collateral estimate, with the weight reflecting the volume of experience.

A credibility framework in which the prior distribution of a risk parameter is updated by observed experience, producing a posterior mean that is a weighted combination of prior mean and sample mean.

A function assigning a numerical value to wealth outcomes that represents preferences; its concavity corresponds to risk aversion, and expected utility ranks uncertain prospects.

A preference for a certain outcome over an uncertain prospect with the same expected value, reflected in a concave utility function and a positive risk premium.

A trading strategy that requires no initial net investment and yields a nonnegative payoff in every state with a strictly positive payoff in at least one state.

A scalar for which a nonzero vector is mapped to a scalar multiple of itself by a square matrix; eigenvalues are roots of the characteristic polynomial.

For a square matrix with nonzero determinant, the unique matrix whose product with it, in either order, is the identity matrix; it is used to solve linear systems.

The derivative of a function of several variables with respect to one variable while holding the others fixed, measuring the function's local rate of change in that direction.