IAI CM2 flashcards

34 cards. Read the term and the definition here. The deck at the top of this page is optional.

Survival function S(x)

Probability that a newborn survives to age x; equals 1 minus the distribution function of the future lifetime random variable and is non-increasing.

Force of mortality

Instantaneous death rate at age x, defined as the density of failure divided by the survival function; equals minus the derivative of log S(x).

Curiate expectation e̊ₓ

Complete expected future lifetime from age x, equal to the integral over t of the survival probability tPx evaluated from age x.

Uniform distribution of deaths

Assumption that deaths are evenly spread within each year of age, giving tQx equal to t times Qx for t between zero and one.

Central death rate mₓ

Deaths in an age interval divided by the central exposed to risk; approximates the force of mortality and links to qx under UDD.

Standardised mortality ratio

Ratio of observed deaths to expected deaths, where expected deaths apply a standard mortality table to the study population's exposure.

Gompertz law

Mortality model with force of mortality equal to B times c to the power x, producing exponentially increasing mortality with age.

Lee-Carter model

Stochastic mortality model expressing log central death rates as an age effect plus an age-sensitivity coefficient times a time index.

Graduation goodness of fit

Chi-square statistic summing squared differences between observed and graduated deaths divided by graduated expected deaths across ages.

Whole life assurance Ax

Expected present value of a unit benefit paid at the end of the year of death, summed over all future years with discounting.

Annuity-due äx

Expected present value of a unit payment at the start of each year while the life survives, equal to the sum of discounted survival probabilities.

Pure endowment nEx

Expected present value of a unit payment made at time n only if the life aged x survives to age x plus n; equals vⁿ times nPx.

Commutation functions

Tabulated quantities Dx, Cx, Nx and Mx built from discounted survivors and deaths, allowing rapid computation of assurance and annuity values.

Equivalence principle

Premium-setting rule equating expected present value of premiums to expected present value of benefits plus expenses at policy inception.

Prospective reserve

Policy value at duration t computed as expected present value of future benefits minus future net premiums, using the equivalence principle.

Fackler recursion

Relationship linking reserves at consecutive durations through interest, survival probability and the death benefit paid during the year.

Zillmerised reserve

Modified reserve that deducts an initial acquisition expense from the first-year reserve, reducing early strain on the insurer.

Normal cost

Actuarial present value of benefits accruing to active members during the current year, used to set the contribution rate.

Defined contribution scheme

Pension arrangement where the benefit depends on accumulated contributions and investment returns, with the member bearing investment risk.

Multiple decrement table

Table modelling several modes of exit simultaneously, with dependent rates derived from independent rates and forces of decrement.

CARE pension scheme

Career average revalued earnings scheme where each year's pension accrues on that year's pensionable salary and is revalued to retirement.

Principle of parsimony

Model-building guideline favouring the simplest model that adequately captures the essential features of the underlying data and process.

Sensitivity analysis

Technique varying one assumption or parameter at a time to measure how much the model output responds to that change.

Model point grouping

Approach of running a representative subset of policies and scaling results, reducing computation while controlling approximation error.

Itô's lemma

Stochastic chain rule giving the differential of a smooth function of a diffusion, including the second-order term involving the squared volatility.

Quadratic variation

Limit of squared increments of a process; for standard Brownian motion over an interval it equals the interval length.

Geometric Brownian motion

Process with proportional increments following Brownian motion, used to model asset prices and giving lognormal distributions.

Itô isometry

Identity equating the expectation of the squared stochastic integral with the expectation of the integrated squared integrand against quadratic variation.

Martingale property

Conditional expectation of a future value given current information equals the current value, representing a fair game.

Girsanov theorem

Result describing how a change of probability measure alters the drift of a Brownian motion while preserving its volatility.

Black-Scholes formula

Closed-form European call price equal to the stock times N(d1) minus discounted strike times N(d2), under lognormal asset dynamics.

Put-call parity

No-arbitrage relationship stating call minus put equals stock price minus discounted strike for European options on the same underlying.

Vasicek model

Mean-reverting Gaussian short-rate model with constant volatility, allowing negative interest rates and yielding affine bond prices.

CIR model

Short-rate model with volatility proportional to the square root of the rate, ensuring non-negativity and an affine term structure.