CAA Fellow Actuary (China) cheat sheet

Under the equivalence principle, the gross premium G solves E[L]=0 where L is the present value of future loss; net premium uses benefits only, gross premium adds expenses and profit margins.

Prospective reserve tV equals E[future benefits + future expenses − future premiums | alive at t]; retrospective reserve equals accumulated past premiums minus accumulated benefits and expenses.

Recursive reserve relation: (tV + G)(1+i) = q_{x+t}·S + p_{x+t}·(t+1V), where S is the sum at risk; this drives policyholder dividend and cash-value mechanics.

For a life annuity-due ä_x = Σ v^k·kPx, and ä_x = (1 − A_x)/d with d = i/(1+i); A_x is the EPV of whole life insurance payable at end of year of death.

Collective risk model: S = Σ X_i, E[S] = λm₁, Var(S) = λm₂; the Cramér–Lundberg approximation gives ψ(u) ≈ C·e^{−Ru} with R the adjustment coefficient solving λ + δ = λ·M_X(R).

Individual risk model: S = Σ I_j·B_j with I_j independent Bernoulli(q_j); Var(S) = Σ q_j(1−q_j)B_j², and the normal approximation applies when no single B_j dominates.

For aggregate claims, Panjer recursion p_n = Σ_{k=1}^{n} (a + bk/n)·p_{n−k}·f_k applies when the frequency distribution satisfies the (a,b,0) class; compound Poisson has a=0, b=λ.

Premium principles: expected value (adds no loading), variance principle P = E[S] + αVar(S), standard deviation principle, exponential principle P = (1/α)ln E[e^{αS}], and Esscher transform; each satisfies different axioms.

Ruin theory: for the compound Poisson surplus U(t) = u + ct − S(t), the net profit condition c > λm₁ is necessary for ψ(u) < 1; ψ(0) = 1/(1+θ) under exponential claims.

Gross premium components: net premium for mortality/interest risk plus expense loadings (per-policy, per-1000 of sum assured, percentage of premium) plus a profit/contingency margin.

Zillmerised reserve tV^Z = tV − (α − α^Z)·ä_{x+t}/ä_x; Zillmer reserve is lower in early durations, letting acquisition costs be recovered without showing negative reserves under China solvency rules.

Under China's new solvency framework (C-ROSS Phase II), life insurance reserves combine a best-estimate liability, a risk margin, and a residual margin (contractual service margin) recognised over coverage.

Mortality basis: use a graduated life table (e.g., China Life Insurance Mortality Table 2010–2013) with q_x, l_x; select mortality adjustments apply for underwritten lives in early durations.

Health insurance reserving: IBNR (incurred but not reported), unearned premium reserve, and ageing reserve for long-term health products; morbidity trend and medical inflation are separate assumptions from interest.

Policyholder dividend mechanics: participating policies allocate divisible surplus under a contribution principle; dividend options include cash, premium reduction, accumulation at interest, and paid-up additions.

Cash value and nonforfeiture: minimum cash value is typically tV less a surrender charge; policy loans accrue interest at a stated rate and reduce the death benefit if unpaid.

China's critical illness definition standard (2020 revision) mandates 28 standardised severe and 3 mild CI definitions, constraining product design and incidence assumptions used in pricing.

Chain-ladder development factor f_k = Σ C_{i,k+1} / Σ C_{i,k}; ultimate for accident year i is C_{i,n−i+1}·Π f_k over remaining periods; requires no development beyond the latest diagonal.

Bornhuetter–Ferguson estimate: Û_i = C_{i,n−i+1} + (1 − 1/Πf_k)·E_i where E_i is an a priori expected ultimate (exposure × expected loss ratio); stabilises immature years.

Mack chain-ladder gives distribution-free standard error of the reserve using recursive formulas on the development factors' weighted variances.

BF and Cape Cod differ in that Cape Cod derives the a priori ultimate from the observed loss ratio of the matured years applied to exposure, rather than an external expected loss ratio.

Premium earning: 1/24 method for monthly policies, 1/8 method for quarterly, 1/365 daily pro rata; unearned premium reserve must be tested for adequacy against expected claims and expenses.

IBNR vs. IBNER: IBNR covers claims not yet reported; IBNER covers deterioration of already-reported claims; case reserves plus IBNR/IBNER form the total claims reserve.

Onerous contract test: if expected ultimate losses plus expenses exceed unearned premium, a premium deficiency reserve is recognised in the current period.

Large loss loading and catastrophe loading: excess-of-loss reinsurance recoveries reduce net retained loss; reinstatement premiums and reinsurance bad debt are separate cash flows.

Defined benefit obligation (DBO): present value of expected future benefit payments attributable to past service, discounted at a high-quality corporate bond rate (or government bond rate where no deep market).

Projected unit credit method attributes benefit to each year of service; current service cost is the increase in DBO from one year's additional service, excluding interest and benefit payments.

Net interest on the net defined benefit liability = discount rate × (DBO − plan assets); remeasurements (actuarial gains/losses, asset returns above interest) go to OCI, not profit or loss.

China's basic pension pillar: urban employee basic pension combines a social pooling component and an individual account; the individual account is credited with a stated annual interest rate.

Funding ratio = plan assets / DBO; a surplus may be subject to an asset ceiling so the recognised net asset cannot exceed the present value of future economic benefits (refunds or contribution reductions).

Settlement and curtailment: a settlement (e.g., lump-sum buyout) recognises gain/loss immediately; a curtailment (e.g., plan amendment reducing benefits) remeasures DBO and recognises the effect in profit or loss.

Actuarial assumptions for pension plans: discount rate, salary growth, mortality, turnover, retirement age, and benefit indexation; sensitivity disclosures are required for each significant assumption.

Social insurance financing: pay-as-you-go systems depend on the dependency ratio (beneficiaries/contributors); ageing populations raise the required contribution rate for a given replacement rate.

Macaulay duration D = Σ t·w_t where w_t = PV(CF_t)/P; modified duration D* = D/(1+y) and ΔP/P ≈ −D*·Δy.

Convexity C = Σ t(t+1)·w_t/(1+y)²; ΔP/P ≈ −D*·Δy + ½·C·(Δy)², which captures the asymmetric price-yield relation.

Immunisation requires matching duration and convexity of assets and liabilities; duration matching alone holds only for small, parallel yield curve shifts.

Key rate duration measures sensitivity to a shift at a specific maturity point, capturing non-parallel curve risk that a single duration number misses.

Cash-flow matching (dedication) eliminates reinvestment and price risk for fixed liabilities but is costly; it is preferred when liabilities are highly predictable.

ALM for life insurers: match long-duration liabilities with long bonds; China's regulators impose duration-gap and asset-liability ratio monitoring to limit mismatch risk.

Yield curve construction: bootstrap zero-coupon rates from coupon bonds, then derive forward rates f_{t,t+1} = (1+z_{t+1})^{t+1}/(1+z_t)^t − 1.

Credit spread risk: spread duration measures price sensitivity to spread changes; expected loss = PD × LGD, and spread ≈ expected loss plus risk premium under a risk-neutral measure.

IFRS 17 / China's new insurance contract standard: measurement = fulfilment cash flows (best estimate + risk adjustment) + contractual service margin (CSM).

CSM is released to profit or loss over the coverage period as services are provided; it is unlocked only for changes in estimates relating to future service, not for financial assumptions in the variable fee approach.

Insurance revenue excludes investment components and deposit components; it is recognised as the insurer provides coverage, based on expected claims and expenses plus CSM release.

General measurement model vs. variable fee approach: VFA applies to direct participating contracts where policyholders share investment returns; the CSM absorbs financial assumption changes.

Premium allocation approach (PAA) is permitted for short-duration contracts (coverage ≤1 year, or where it approximates the GMM); liability for remaining coverage plus incurred claims liability.

China Accounting Standards for Business Enterprises (CAS 25) insurance contracts and C-ROSS solvency reports differ in measurement basis; reconciliation between statutory, accounting, and solvency figures is required.

Deferred acquisition costs (DAC) under older GAAP are amortised in proportion to premium; under IFRS 17 acquisition cash flows are included in the fulfilment cash flows and released with the CSM.

Financial statement analysis: combined ratio = loss ratio + expense ratio; a combined ratio above 100% indicates an underwriting loss, offset by investment income.

Insurable interest: the policyholder must have a legally recognised interest in the subject matter at inception; for life insurance, consent of the insured is required for policies on another person's life.

Utmost good faith (duty of disclosure): the applicant must disclose material facts the insurer would consider in underwriting; Chinese Insurance Law allows the insurer to rescind within 2 years of contract formation for fraudulent non-disclosure.

Incontestability: after 2 years from contract formation, the insurer cannot rescind a life policy for misrepresentation or non-disclosure, except for fraud discovered within that period.

Indemnity principle applies to non-life insurance; life insurance benefits are not limited to indemnity, so multiple policies may pay in full.

Subrogation: after paying a claim, the insurer may step into the insured's rights against a third-party tortfeasor, but cannot recover more than the amount paid.

Regulatory capital in China: C-ROSS requires insurers to maintain minimum capital (MCAR) and comprehensive solvency ratios; the core and comprehensive solvency ratios are monitored quarterly.

Professional ethics: actuarial standards require independence, objectivity, disclosure of conflicts, and clear communication of assumptions and uncertainty; certification of reserve adequacy is a formal opinion.

Market conduct: China's regulator prohibits misleading sales illustrations, requires disclosure of exclusions, and mandates a 15-day cooling-off period for life policies.

Risk categories in an insurer's ORSA: insurance risk, market risk, credit risk, liquidity risk, operational risk, and strategic/reputational risk; the ORSA links risk profile to capital needs.

Economic capital is the capital needed to cover unexpected losses at a target confidence level over a horizon; it equals the difference between a high quantile and the expected loss.

Solvency II-style SCR = base solvency capital requirement + operational risk, adjusted for loss-absorbing capacity of deferred taxes and technical provisions; China's C-ROSS uses a comparable modular approach.

Risk aggregation: under perfect correlation SCR = Σ SCR_i; under independence SCR = √(Σ SCR_i²); actual aggregation uses a correlation matrix and is between these bounds.

Diversification benefit = Σ standalone capital − aggregate capital; it must be measured with a consistent risk measure (VaR or TVaR) and confidence level.

Capital allocation methods: proportional to standalone capital, marginal (Euler) allocation, and Shapley value; Euler allocation is consistent with VaR/TVaR for homogeneous risk measures.

Reinsurance as capital management: quota share and surplus treaties transfer proportional risk and free capital; excess-of-loss reduces tail risk and lowers required capital per unit of exposure.

Liquidity risk management: maintain a liquidity buffer of high-quality liquid assets; stress test for mass surrender, catastrophe claims, and collateral calls simultaneously.

Model governance: document purpose, scope, assumptions, data sources, validation, and limitations; independent review and change control are required for models used in reserving and capital.

Model validation tests: back-testing (actual vs. expected), sensitivity analysis, scenario testing, and comparison with alternative methods (e.g., chain-ladder vs. BF).

Data quality checks: reconcile to source systems, test for missing values, outliers, duplicates, and consistency of definitions across periods; document any adjustments.

Generalised linear models for claims: Tweedie distribution with log link for pure premium, Poisson for frequency with log exposure offset, and Gamma for severity.

Credibility theory: Bühlmann credibility Z = n/(n+k) with k = EPV/VHM; the credibility estimate is Z·(observed) + (1−Z)·(prior mean).

Machine learning in actuarial work: gradient boosting and random forests improve predictive accuracy but require explainability, fairness testing, and monitoring for model drift.

Communication: an actuarial report should state the question, data, method, key assumptions, results with uncertainty ranges, sensitivity to key assumptions, and limitations.

Presenting uncertainty: use ranges rather than point estimates; state the confidence level and time horizon for capital figures, and disclose material model changes separately.

Model governance: document purpose, scope, assumptions, data sources, validation, and limitations; independent review and change control are required for models used in reserving and capital.

Model validation tests: back-testing (actual vs. expected), sensitivity analysis, scenario testing, and comparison with alternative methods (e.g., chain-ladder vs. BF).

Data quality checks: reconcile to source systems, test for missing values, outliers, duplicates, and consistency of definitions across periods; document any adjustments.

Generalised linear models for claims: Tweedie distribution with log link for pure premium, Poisson for frequency with log exposure offset, and Gamma for severity.

Credibility theory: Bühlmann credibility Z = n/(n+k) with k = EPV/VHM; the credibility estimate is Z·(observed) + (1−Z)·(prior mean).

Machine learning in actuarial work: gradient boosting and random forests improve predictive accuracy but require explainability, fairness testing, and monitoring for model drift.

Communication: an actuarial report should state the question, data, method, key assumptions, results with uncertainty ranges, sensitivity to key assumptions, and limitations.

Presenting uncertainty: use ranges rather than point estimates; state the confidence level and time horizon for capital figures, and disclose material model changes separately.