Actuarium

Exams

Study guides, original practice questions with worked solutions, and past-paper strategy for every CAS, SOA and CPCU exam — each linked to the Library so you study the concept, not just the syllabus.

43 exams & requirements361 practice questionsKaTeX-rendered solutions

Casualty Actuarial Society — ACAS and FCAS for property & casualty.

Preliminary

Exam 1 Probability (P)

Preliminary

Exam P/1 tests calculus-based probability: set theory, conditional probability and Bayes, discrete and continuous univariate distributions, transformations, moment generating functions, and joint/conditional/marginal distributions. It is shared with the SOA and is the usual first exam.

30 multiple-choice3 hours300 study hrs9 MC · 2 written

Exam 2 Financial Mathematics (FM)

Preliminary

Exam FM/2 covers interest theory: accumulation functions, nominal and effective rates, annuities, loan amortization and sinking funds, bond pricing and amortization, yield curves and spot/forward rates, duration, convexity, and immunization. Derivatives were removed from the FM syllabus in 2022; the emphasis is now firmly on cash-flow valuation.

30 multiple-choice2.5 hours250 study hrs9 MC · 2 written

MAS-I Modern Actuarial Statistics I

Preliminary

MAS-I covers Poisson processes and Markov chains, survival and reliability, parametric estimation and hypothesis testing, GLMs with an actuarial lens, and ARIMA time-series basics. It is the first exam with an explicit modeling mindset.

45 multiple-choice4 hours350 study hrs9 MC · 2 written

MAS-II Modern Actuarial Statistics II

Preliminary

MAS-II is the credibility and modern-modeling exam: classical and Bayesian credibility, conjugate priors and MCMC diagnostics, penalized regression, tree ensembles, and linear mixed models as a generalization of Bühlmann–Straub.

45 multiple-choice4 hours350 study hrs9 MC · 2 written

Associateship (ACAS)

Fellowship (FCAS)

Non-exam requirement

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Choose your exam, dates and weekly time blocks. The builder weights weeks by syllabus topic, reserves the final 15% for review and mock exams, and tracks every session you complete.

Pick your study days; block lengths are scaled to hit your weekly target.

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Suggested timeline: 40 weeks at 8 h/week (≈350 recommended hours incl. 15% review)

TopicWeightHoursResourcesPractice
FAM-S: Insurance & reinsurance coverages
  • Describe common short-term insurance and reinsurance contract types, including quota-share, surplus-share, excess-of-loss and facultative arrangements.
  • Apply policy limits, deductibles, coinsurance and coverage modifications to loss payments for a single claim.
  • Determine insurer vs. reinsurer retained losses under proportional and non-proportional treaties.
  • Identify the effect of policy provisions (aggregate limits, per-occurrence limits) on ceded and retained loss distributions.
4%12 0 MC · 1 written
FAM-S: Severity, frequency & aggregate models
  • Compute moments, percentiles and limited expected values for common severity distributions (Pareto, gamma, lognormal, Weibull, exponential).
  • Apply deductibles, limits, coinsurance and inflation to severity distributions and derive the resulting payment-per-loss and payment-per-payment distributions.
  • Compute the distribution, mean and variance of aggregate claims via the compound (Poisson, negative binomial, binomial) frequency-severity model.
  • Use the recursive (Panjer) method and moment-based approximations (normal, lognormal, translated gamma) to approximate aggregate loss distributions.
20%60 2 MC
FAM-S: Parametric estimation
  • Fit parametric loss models by the method of moments and maximum likelihood, including for grouped, censored and truncated data.
  • Construct and interpret the likelihood function for data subject to policy limits and deductibles.
  • Apply the delta method and observed/expected Fisher information to estimate variances of MLE parameter estimates.
  • Use graphical and hypothesis-based goodness-of-fit tools (Q-Q plots, chi-square, Kolmogorov-Smirnov) to select among competing models.
9%27 1 MC
FAM-S: Introductory credibility
  • Apply limited fluctuation (classical) credibility to determine the standard for full credibility and partial credibility factors.
  • Compute Bühlmann and Bühlmann-Straub credibility premiums from expected value of process variance and variance of hypothetical means.
  • Estimate credibility parameters (k, Z) from sample data using nonparametric and semiparametric methods.
  • Interpret credibility-weighted estimates as a blend between individual experience and a manual/collective rate.
4%12 1 MC
FAM-S: Pricing & reserving for short-term insurance
  • Adjust historical premium to current rate level and trend losses to the future policy period.
  • Estimate ultimate losses using the chain-ladder, Bornhuetter-Ferguson and expected-loss-ratio reserving methods.
  • Calculate the indicated overall rate change combining loss ratio and pure premium approaches.
  • Evaluate the impact of reinsurance and loss development assumptions on indicated reserves and rates.
7%21 1 MC
FAM-S: Option pricing fundamentals
  • Price European put and call options using put-call parity and the binomial lattice model.
  • Apply risk-neutral valuation and the Black-Scholes formula to value simple derivatives.
  • Describe how embedded options in insurance products (guarantees, caps, floors) can be decomposed into vanilla option positions.
  • Compute the delta of an option position and construct a simple replicating/hedging portfolio.
6%18 1 MC
FAM-L: Long-term insurance coverages
  • Describe the benefit structure of whole life, term, endowment, and deferred insurance and annuity contracts.
  • Translate verbal descriptions of long-term coverage provisions into actuarial present value expressions.
  • Distinguish level, increasing and decreasing benefit patterns and their effect on reserves and premiums.
  • Identify how riders (e.g., waiver of premium, accidental death) modify the basic contract's cash flows.
5%15 0 MC · 1 written
FAM-L: Survival models
  • Define the survival function, force of mortality, and curtate/complete expectation of life, and relate them algebraically.
  • Compute probabilities and moments of time-to-death and time-to-failure under standard parametric mortality laws (constant force, De Moivre, Gompertz, Makeham) and life tables.
  • Apply select-and-ultimate mortality tables and fractional-age assumptions (uniform distribution of deaths, constant force) to interpolate probabilities.
  • Compute probabilities for multiple lives (joint life, last survivor) under independence assumptions.
12%36 1 MC
FAM-L: Present value random variables
  • Derive the distribution and moments of the present value random variable for insurances and annuities payable continuously, annually or mthly.
  • Apply the relationships between insurance and annuity APVs (e.g., $A=1-d\ddot a$) to simplify calculations.
  • Compute actuarial present values under a fully discrete, fully continuous, or semicontinuous model.
  • Use recursive relationships to compute actuarial present values for benefits deferred or paid at the end/beginning of the year of death.
10%30 1 MC
FAM-L: Premium calculation
  • Apply the equivalence principle to determine net premiums for insurances and annuities under various benefit and premium timing patterns.
  • Incorporate expenses (percent of premium, per-policy, per-unit) to compute gross premiums.
  • Compute the variance of loss-at-issue random variables for premium-paying contracts.
  • Apply premium refund/return-of-premium and percentile premium principles to alternative premium calculations.
10%30 1 MC
FAM-L: Reserves (policy values)
  • Compute prospective and retrospective policy values (reserves) for standard insurance and annuity contracts.
  • Apply the recursive reserve relationship to project reserves forward one year and decompose gains by source.
  • Compute Fackler's accumulation formula and full/modified preliminary term reserves.
  • Interpret the relationship between reserves, premiums and expected mortality/interest gains.
10%30 1 MC
FAM-L: Interest-rate risk & pension intro
  • Describe key duration and convexity measures and apply them to assess a portfolio's exposure to interest-rate movements.
  • Apply immunization (Redington and full immunization) techniques to match asset and liability cash flows.
  • Describe the basic structure of defined-benefit and defined-contribution pension plans and their funding objectives.
  • Compute simple pension actuarial liabilities under a career-average or final-salary benefit formula.
3%9 1 MC

12 weeks · 96 planned hours for SOA FAM · recommended ≈350 hrs (254 short)

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