MAS-I flashcards

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

Principle of indemnity

The insured is restored to approximately the pre-loss financial position, and recovery cannot exceed the actual loss. Valued policies and replacement-cost coverage are the standard exceptions.

Insurable interest

A legal right in the subject matter such that its loss causes financial detriment. Required at policy inception for life insurance and at the time of loss for property insurance.

Adverse selection

The tendency of higher-than-average risks to purchase or retain coverage at a given price, which can force premiums above the level low-risk insureds will accept.

Moral hazard

An insurance-induced change in behavior that increases expected loss or claim cost. Deductibles, coinsurance, policy limits, and exclusions are used to control it.

Combined ratio

The loss ratio plus the expense ratio. A value below 1.00 indicates an underwriting profit; a value above 1.00 indicates an underwriting loss before investment income.

Prior approval filing

A rate filing method in which the insurer must obtain regulator approval of proposed rates before using them. It is the strictest of the common filing methods.

Risk-based capital ratio

Total adjusted capital divided by the authorized control level derived from asset, credit, underwriting, and other risk charges. Prescribed ratio thresholds trigger escalating regulatory action levels.

Guaranty association

A state-mandated mechanism that pays covered claims of insolvent insurers up to statutory limits, funded by assessments levied on insurers licensed in the state.

Bayes' theorem

P(A|B) = P(B|A)P(A)/P(B). It converts a prior probability into a posterior probability by weighting with the likelihood, and underlies Bayesian and credibility estimation.

Moment generating function

M_X(t) = E[e^{tX}]. Its derivatives evaluated at zero yield the moments of X, and if it exists in a neighborhood of zero it uniquely determines the distribution.

Law of total variance

Var(X) = E[Var(X|Y)] + Var(E[X|Y]). It splits total variability into the average within-group variance plus the variance of conditional means across groups.

Memoryless property

For an exponential variable, P(X > s + t | X > s) = P(X > t). Elapsed waiting time gives no information about remaining waiting time. The geometric distribution shares this property.

Factorization theorem

A statistic T(X) is sufficient for a parameter if and only if the joint density can be written as g(T(x), θ) times h(x), separating the parameter-dependent factor from the data-only factor.

Cramér-Rao lower bound

Any unbiased estimator satisfies Var(θ̂) ≥ 1/(n·I₁(θ)), where I₁(θ) is the Fisher information in a single observation. It sets the benchmark for estimator efficiency.

Delta method

A technique for approximating the variance of a smooth function of an estimator: Var(g(θ̂)) ≈ [g'(θ)]²·Var(θ̂), obtained by linearizing g around the true parameter value.

Central limit theorem

Standardized sums of independent, identically distributed random variables with finite variance converge to a standard normal distribution, enabling normal approximations to aggregate loss distributions.

Annuity-immediate present value

a_n = (1 − v^n)/i, the value today of one unit paid at the end of each of n periods, where v = 1/(1 + i) is the one-period discount factor.

Annuity-due present value

ä_n = (1 − v^n)/d with d = i/(1 + i). It equals (1 + i)·a_n because each of the n payments occurs one period earlier than under an annuity-immediate.

Force of interest

The continuously compounded rate δ satisfying δ = ln(1 + i). The accumulation function from time zero to t equals exp of the integral of the force of interest over that interval.

Macaulay duration

The present-value-weighted average time of the cash flows, D = Σ t·CF_t·v^t / P. It measures price sensitivity and the horizon where price and reinvestment risks offset.

Modified duration

D* = D/(1 + i). For small changes in yield, the percentage price change is approximately −D*·Δi, allowing price sensitivity to be estimated without repricing the instrument.

Convexity adjustment

For a yield change Δi, ΔP/P ≈ −D*·Δi + ½·C·(Δi)², where convexity C = Σ t(t+1)·CF_t·v^(t+2)/P. It corrects duration estimates for larger yield movements.

Redington immunization

Protection of surplus requiring PV(assets) equal to PV(liabilities), asset duration equal to liability duration, and asset convexity at least as large as liability convexity.

Forward rate

A rate agreed now for a future period, implied by spot rates. With annual spots, (1 + s₂)² = (1 + s₁)(1 + f₁,₂), so the forward rate solves for the missing factor.

Collective risk model

S = X₁ + ⋯ + X_N, where the claim count N is independent of the identically distributed severities. Then E[S] = E[N]E[X] and Var(S) = E[N]Var(X) + Var(N)(E[X])².

Compound Poisson variance

When the claim count is Poisson with mean λ, Var(S) = λ·E[X²] = λ(Var(X) + (E[X])²) and E[S] = λ·E[X], so variance depends on both moments of severity.

Panjer recursion

A recursive formula for aggregate probabilities when severities lie in the (a, b, 0) class: p_n = Σ (a + b·k/n)·f_k·p_{n−k}, initialized at p₀ and iterated upward.

Net profit condition

The condition c > λ·E[X], meaning premium income per unit time exceeds expected claim cost per unit time, giving the surplus process positive drift and ruin probability below one.

Adjustment coefficient

The positive nonzero solution R of λ + c·R = λ·M_X(R) for a compound Poisson surplus process. Lundberg's inequality then bounds the ruin probability by e^(−Ru).

Bühlmann credibility factor

Z = n/(n + k) with k = E[Var(X|θ)] / Var(E[X|θ]). The credibility estimate is Z times the sample mean plus (1 − Z) times the prior mean.

Loss elimination ratio

LER = E[X∧d]/E[X], the fraction of expected ground-up loss removed by applying a deductible d. It complements the expected deductible payment E[(X − d)+].