Learning path
Actuarial Science learning path: everything to study, topic by topic
Comprehensive actuarial science assessment covering probability and statistics, life contingencies, property and casualty insurance, financial mathematics, pricing and product design, enterprise risk management, and expert actuarial topics including IFRS 17 and stochastic modeling.
Short answer
To learn Actuarial Science, work through 7 modules and 20 topics in the order they build on each other. It starts with Probability & Statistics, then moves on to Life Contingencies and Property & Casualty. Use the map as a checklist, or measure your level and study only what is missing.
What you will study
Topics are grouped by module. Open one to see its objectives and key concepts.
1 · Probability & Statistics3 topics
Probability Distributions
Common actuarial distributions — Poisson, negative binomial, gamma, lognormal, Pareto — and their applications to frequency and severity modeling
Objectives
- Select appropriate frequency and severity distributions for insurance data
- Fit parameters using maximum likelihood estimation and method of moments
Key concepts
- Poisson distribution
- negative binomial
- gamma distribution
- lognormal distribution
- Pareto distribution
- frequency-severity split
Statistical Estimation
Maximum likelihood estimation, method of moments, Bayesian estimation, hypothesis testing, and confidence intervals in actuarial contexts
Objectives
- Apply MLE and MoM to estimate distribution parameters from claims data
- Evaluate model adequacy using goodness-of-fit tests (chi-square, K-S, A-D)
Key concepts
- maximum likelihood estimation
- method of moments
- Bayesian estimation
- hypothesis testing
- confidence intervals
- goodness-of-fit tests
Survival Models
Survival functions, hazard rates, Kaplan-Meier estimation, Cox proportional hazards, and censoring in mortality and lapse studies
Objectives
- Construct and interpret Kaplan-Meier survival curves from policyholder data
- Distinguish between right, left, and interval censoring and their implications
Key concepts
- survival function S(x)
- hazard rate
- force of mortality
- Kaplan-Meier estimator
- Cox proportional hazards
- censoring
2 · Life Contingencies3 topics
Life Tables & Mortality
Construction and interpretation of life tables — qx, lx, dx, ex, mortality laws (Gompertz, Makeham), and select-and-ultimate tables
Objectives
- Construct a life table from raw mortality data and interpolate between integer ages
- Compare Gompertz and Makeham mortality models and explain when each applies
Key concepts
- qx (mortality rate)
- lx (survivors)
- dx (deaths)
- ex (life expectancy)
- Gompertz law
- Makeham law
- select-and-ultimate
Life Annuities
Whole life, temporary, deferred, and increasing annuities — present values, commutation functions, and annuity-due vs annuity-immediate
Objectives
- Calculate actuarial present values of whole life and temporary annuities
- Apply commutation functions to simplify annuity calculations
Key concepts
- whole life annuity
- temporary annuity
- deferred annuity
- annuity-due vs annuity-immediate
- commutation functions (Dx, Nx)
- present value of annuity
Life Insurance Products
Term, whole life, endowment, and universal life insurance — net premiums, benefit reserves, and policy values using the equivalence principle
Objectives
- Calculate net premiums and benefit reserves for standard life insurance products
- Explain the equivalence principle and reconcile prospective and retrospective reserves
Key concepts
- term life insurance
- whole life insurance
- endowment insurance
- net premium
- benefit reserve
- equivalence principle
- prospective vs retrospective reserve
3 · Property & Casualty3 topics
Loss Distributions & Severity
Aggregate loss models, compound frequency-severity, excess loss, limited expected value, and loss elimination ratios
Objectives
- Model aggregate losses using compound frequency-severity distributions
- Calculate the impact of deductibles and policy limits on expected losses
Key concepts
- aggregate loss model
- compound Poisson
- excess loss
- limited expected value
- loss elimination ratio
- deductible impact
Reserving Methods
Chain-ladder, Bornhuetter-Ferguson, Cape Cod, IBNR estimation, loss development triangles, and tail factor selection
Objectives
- Apply chain-ladder and BF methods to a loss development triangle and compare results
- Explain when BF is preferred over chain-ladder and the assumptions behind each
Key concepts
- chain-ladder method
- Bornhuetter-Ferguson (BF) method
- Cape Cod method
- IBNR (incurred but not reported)
- loss development triangle
- tail factor
- development factor
Reinsurance
Proportional (quota share, surplus) and non-proportional (XoL, stop-loss) reinsurance, retrocession, and ceded premium calculation
Objectives
- Design a reinsurance programme that balances risk transfer with cost efficiency
- Calculate ceded premiums and net retention under proportional and non-proportional structures
Key concepts
- quota share
- surplus treaty
- excess-of-loss (XoL)
- stop-loss
- retrocession
- ceded premium
- retention
4 · Financial Mathematics3 topics
Time Value of Money
Compound interest, present and future values, annuities-certain, yield curves, and spot/forward rates in actuarial valuation
Objectives
- Calculate present and future values of complex cash flow streams
- Derive forward rates from a spot rate curve and interpret the term structure
Key concepts
- compound interest
- present value
- future value
- annuity-certain
- yield curve
- spot rate
- forward rate
Interest Rate Models
Vasicek, Cox-Ingersoll-Ross, Black-Karasinski models, yield curve construction, and stochastic interest rate scenarios
Objectives
- Calibrate a mean-reverting interest rate model to market data
- Compare Vasicek and CIR models and explain when negative rates are acceptable
Key concepts
- Vasicek model
- CIR model
- Black-Karasinski
- mean reversion
- stochastic interest rates
- yield curve fitting
Asset-Liability Management
Duration matching, immunization, cash flow matching, convexity, and ALM strategies for insurance portfolios
Objectives
- Construct an immunized portfolio that protects surplus against parallel yield curve shifts
- Evaluate the limitations of duration matching and when convexity adjustment is necessary
Key concepts
- Macaulay duration
- modified duration
- convexity
- immunization
- cash flow matching
- surplus optimization
- key rate duration
5 · Pricing & Product Design3 topics
Ratemaking
Loss ratio method, pure premium method, on-leveling, trending, expense loading, and profit provision in insurance pricing
Objectives
- Calculate an indicated rate change using both loss ratio and pure premium methods
- Apply on-leveling and trending adjustments to historical loss data
Key concepts
- loss ratio method
- pure premium method
- on-leveling
- trending
- expense loading
- profit provision
- combined ratio
Experience Rating
Individual risk rating, retrospective rating, schedule rating, experience modification factors, and large deductible plans
Objectives
- Calculate an experience modification factor from historical loss and payroll data
- Design a retrospective rating plan with appropriate minimum and maximum premiums
Key concepts
- experience modification factor
- retrospective rating
- schedule rating
- loss-sensitive plans
- large deductible
- burning cost
Credibility Theory
Classical, Buhlmann, and Buhlmann-Straub credibility models, full credibility standards, and GLM-based pricing approaches
Objectives
- Apply Buhlmann and Buhlmann-Straub credibility to combine class and individual experience
- Determine full credibility standards for frequency and severity data
Key concepts
- limited fluctuation credibility
- Buhlmann credibility
- Buhlmann-Straub
- full credibility standard
- credibility-weighted estimate
- GLM pricing
6 · Enterprise Risk Management3 topics
Risk Measures
Value-at-Risk, Tail Value-at-Risk (TVaR/CTE), coherent risk measures, risk aggregation, and correlation structures
Objectives
- Calculate VaR and TVaR for common loss distributions and explain why TVaR is coherent
- Apply copulas to model dependence between risk classes in an aggregate portfolio
Key concepts
- Value-at-Risk (VaR)
- Tail Value-at-Risk (TVaR)
- conditional tail expectation (CTE)
- coherent risk measures
- subadditivity
- copulas
Capital Modeling
Solvency Capital Requirement (SCR), Minimum Capital Requirement (MCR), internal models, economic capital, and ORSA
Objectives
- Calculate SCR using the Solvency II standard formula and explain its risk modules
- Compare standard formula vs internal model approaches and their regulatory implications
Key concepts
- SCR (Solvency Capital Requirement)
- MCR (Minimum Capital Requirement)
- economic capital
- internal model
- standard formula
- ORSA
- risk margin
Regulatory Frameworks
Solvency II pillars, NAIC RBC, IAIS ICS, governance requirements, actuarial function holder role, and regulatory reporting
Objectives
- Explain the three pillars of Solvency II and their practical implications
- Compare Solvency II, NAIC RBC, and IAIS ICS in terms of capital calculation methodology
Key concepts
- Solvency II three pillars
- NAIC RBC
- IAIS ICS
- actuarial function holder
- own funds
- regulatory capital ladder
7 · Expert Actuarial2 topics
Advanced Stochastic Modeling
Monte Carlo simulation, nested stochastics, proxy models (curve fitting, LSMC), real-world vs risk-neutral scenarios, and model validation
Objectives
- Design a nested stochastic simulation framework for Solvency II SCR calculation
- Evaluate trade-offs between full nested simulation, LSMC, and curve-fitting proxy models
Key concepts
- Monte Carlo simulation
- nested stochastics
- least-squares Monte Carlo (LSMC)
- proxy models
- real-world vs risk-neutral
- economic scenario generator (ESG)
- model validation
IFRS 17 Accounting
Contractual Service Margin (CSM), risk adjustment, General Measurement Model, Variable Fee Approach, Premium Allocation Approach, and transition
Objectives
- Walk through the IFRS 17 General Measurement Model including initial recognition and subsequent measurement
- Explain CSM amortization, onerous contract treatment, and the choice between GMM, VFA, and PAA
Key concepts
- Contractual Service Margin (CSM)
- risk adjustment
- General Measurement Model (GMM)
- Variable Fee Approach (VFA)
- Premium Allocation Approach (PAA)
- fulfilment cash flows
- onerous contracts
Levels: Junior, Mid, Senior, and Expert
Explain it in your own words
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Frequently asked questions
Where should I start studying Actuarial Science?
Start with Probability & Statistics: Probability Distributions, Statistical Estimation, and Survival Models. The map orders topics by what they depend on, so each one prepares the next.
How long does a full Actuarial Science assessment take?
A full assessment of this path takes about 55 minutes. Study time depends on where you start; a diagnostic shows which topics you can skip.
Do I need an account to use this page?
No. The map, objectives and key concepts are open. You only need an account to be measured, get your gap by topic and receive a plan.