CAS Exam 8 flashcards
CAS Exam 8 · Build recall with a focused review session.
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- Loss elimination ratio
- LER(d) = LEV(d)/E[X], the fraction of ground-up expected loss removed by a deductible d. The deductible credit is 1 − LER(d) applied to expected loss.
- Limited expected value
- LEV(d) = E[min(X,d)] = ∫₀^d S(x)dx. It caps each loss at d, letting increased limits factors and deductible credits be computed without explicitly modeling the tail beyond d.
- Increased limits factor
- ILF(d) = LEV(d)/LEV(b) relative to a base limit b. ILFs are ratios, not increments, so a layer factor for (a,b] is [LEV(b) − LEV(a)]/LEV(base).
- Experience modification formula
- M = (Ap + Ee·w)/(Ep + Ee·w), where Ap is actual limited losses, Ep expected limited losses, Ee expected excess losses, and w the credibility weight placed on excess experience.
- Excess credibility weight
- w = Ee/(Ee + Ep·k) with k = (1−Z)/Z. It blends actual and expected excess experience, giving more weight to actual excess losses when excess experience is credible.
- Bühlmann credibility factor
- Z = n/(n+k) where k = EPV/VHM. EPV is expected process variance within a risk and VHM the variance of hypothetical means across risks; greater heterogeneity raises Z.
- Square-root credibility
- Z = √(N/N_full) for frequency or √(P/P_full) for aggregate loss, capped at 1. It reflects that credibility grows with the square root of exposure, not linearly.
- Expected process variance
- EPV is the average within-risk variance of loss experience, the numerator-side noise in Bühlmann credibility. It measures variability that persists even when a risk's true mean is known.
- Variance of hypothetical means
- VHM is the between-risk variance of true expected loss levels. It is the signal in Bühlmann credibility; a larger VHM relative to EPV increases the credibility assigned to a risk's own experience.
- Franchise deductible cost
- With a franchise deductible d, the insurer pays the full loss once it exceeds d and nothing otherwise. Expected cost equals E[X·1{X>d}], which is E[X] minus LEV(d) plus d·S(d).
- Excess ratio method
- r = (Ap_x + k·Ee_x)/(Ep_x + k·Ee_x), blending actual and expected excess experience with k = (1−Z)/Z. It produces an excess loss provision when excess data are sparse.
- Deductible credit
- The reduction in expected loss from imposing deductible d, equal to 1 − LER(d) applied to ground-up expected loss. It reflects losses eliminated because they fall below the deductible.
- Ground-up loss
- Loss before applying deductibles or limits, used as the base for LER, LEV, and ILF calculations. Ratemaking builds from ground-up expected loss and applies deductible and limit adjustments in sequence.
- Policy limit credit
- The reduction from capping losses at a policy limit L, equal to 1 − ILF(L) relative to unlimited or high-limit expected loss. It prices the tail risk the insurer does not bear.
- Aggregate deductible
- A deductible applied to total losses over a period rather than per loss. Expected cost requires the distribution of aggregate losses, not just the severity distribution, so simulation or aggregate models are used.
- Loss constant
- A flat dollar amount added to premium to cover expenses of handling small losses below a deductible, preserving the deductible credit's accuracy for low-frequency, low-severity risks.
- Trend in ratemaking
- Projected loss trend adjusts historical losses to the future policy period using frequency and severity trends, often selected separately and compounded over the trend period from average loss date.
- On-level factor
- A factor that restates historical premium at current rate levels so that loss ratios reflect current rates. It equals current rate level divided by the average rate level during the experience period.
- Parallelogram method
- A technique for computing the average rate level in an experience period when rates changed mid-period, weighting each rate level by the earned exposure it applies to.
- Loss ratio method
- Indicated rate change = (projected loss ratio)/(target loss ratio) − 1, where projected loss ratio uses on-level premium and trended losses. It complements the pure premium method.
- Pure premium method
- Indicated rate = (trended, developed, on-level losses)/(projected exposure) plus fixed expenses, divided by (1 − variable expense ratio). It builds rates from loss costs directly.
- Loss development factor
- A factor applied to losses at a given maturity to estimate their ultimate value. Ratemaking uses development factors to bring immature experience-period losses to an ultimate basis.
- Credibility complement
- The weight (1−Z) given to the complement of credibility, such as expected loss or a related class, when a risk's own experience is not fully credible.
- Complement of credibility
- The external estimate combined with a risk's own experience in a credibility-weighted rate. Common complements include class expected loss, pooled experience, or a prior rate.
- Classification ratemaking
- Setting relativities by rating variable so that risks with similar expected loss pay similar premium. Relativities are estimated with loss ratios or GLMs and balanced to a base level.
- Generalized linear model
- A regression framework with a distribution family and link function, used to estimate classification relativities. Log link with Poisson or Tweedie errors is standard for frequency and pure premium.
- Tweedie distribution
- A compound Poisson-gamma distribution with a point mass at zero, used for pure premium GLMs because it models both the probability of a claim and its severity in one model.
- Offset in frequency model
- A term with a fixed coefficient of one, typically log(exposure), included in a Poisson frequency GLM so that predicted counts scale with exposure rather than being modeled as a rate.
- Deductible versus retention
- A deductible is subtracted from each loss before payment; a retention is the amount the insured absorbs in aggregate under a self-insurance arrangement. They are priced with different expected-cost formulas.
- Increased limits table
- A set of ILFs by limit derived from a fitted severity distribution or empirical limited expected values, used to price policy limits above the base limit.
- Rate change versus rate level
- A rate change is the percentage adjustment to current rates; the rate level is the resulting average price of coverage. On-leveling restates historical premium to a common rate level.
- Risk load
- An addition to expected loss that compensates for uncertainty and capital tied to a risk. It grows with the variance or tail of the loss distribution and is larger for volatile or high-limit risks.