Actuary Course

Lesson 1 • Descriptive Statistics for Actuaries

Covers measures of central tendency, dispersion, and data visualisation relevant to actuarial datasets. Prepares learners for statistical inference in later chapters.

Lesson 2 • Core Probability Concepts

Introduces sample spaces, events, and probability axioms as the foundation for risk modelling. Directly supports later chapters on loss distributions.

Lesson 3 • Introduction to Financial Mathematics

Establishes time value of money, interest rates, and present value as prerequisites for life and casualty pricing. Links mathematics to financial decision-making.

Lesson 4 • The Actuarial Profession Overview

Defines the actuarial role across insurance, pensions, and finance. Establishes professional context before technical content begins.

Lesson 1 • Discrete Probability Distributions

Covers Poisson, binomial, and negative binomial distributions for modelling claim counts. Connects frequency modelling to aggregate loss calculations.

Lesson 2 • Aggregate Loss Models

Combines frequency and severity distributions into aggregate loss models using convolution and Panjer recursion. Directly enables premium and reserve calculations.

Lesson 3 • Moments and Generating Functions

Derives moments, moment generating functions, and probability generating functions for key distributions. Supports analytical computation of aggregate loss statistics.

Lesson 4 • Continuous Loss Distributions

Examines exponential, gamma, Pareto, and lognormal distributions for severity modelling. Provides tools for selecting distributions based on tail behaviour.

Lesson 1 • Stochastic Interest Rate Models

Introduces short-rate models including Vasicek and Cox-Ingersoll-Ross for stochastic valuation. Prepares learners for option pricing and embedded guarantee valuation.

Lesson 2 • Bond Pricing and Yield Measures

Prices coupon bonds, computes yield to maturity, and analyses price-yield relationships. Provides tools for fixed-income portfolio management.

Lesson 3 • Term Structure of Interest Rates

Analyses spot rates, forward rates, and yield curves as tools for valuing fixed-income cash flows. Connects interest theory to bond pricing and liability valuation.

Lesson 4 • Immunisation and Asset-Liability Matching

Applies duration matching and full immunisation to protect surplus against interest rate shifts. Connects interest theory to actuarial balance sheet management.

Lesson 1 • Survival Models and Life Tables

Introduces the survival function, hazard rate, and curtate future lifetime as core mortality modelling tools. Establishes notation used throughout life contingencies.

Lesson 2 • Multiple Decrement Models

Extends single-decrement life tables to multiple causes of exit such as death, disability, and withdrawal. Enables pricing of products with competing risks.

Lesson 3 • Life Annuity Valuation

Values life-contingent annuities including whole life, temporary, and deferred annuities. Supports pension and retirement product pricing in later applied chapters.

Lesson 4 • Net Premiums and Benefit Reserves

Derives net premiums using the equivalence principle and computes prospective and retrospective reserves. Provides the basis for statutory reserve calculations.

Lesson 1 • Bühlmann and Bühlmann-Straub Models

Derives the Bühlmann credibility formula and extends it to the Bühlmann-Straub model for varying exposure. Provides the industry-standard linear credibility estimator.

Lesson 2 • Trend and Development Adjustments

Applies loss trend factors and loss development triangles to project ultimate losses for ratemaking. Ensures premiums reflect future expected costs.

Lesson 3 • Insurance Ratemaking Fundamentals

Covers the pure premium and loss ratio methods for computing indicated rate changes. Connects credibility estimates to practical premium adjustments.

Lesson 4 • Classification Ratemaking and GLMs

Uses generalised linear models to estimate relativities for rating variables such as age and territory. Extends manual ratemaking to multivariate classification systems.

Lesson 1 • Reserve Adequacy and Validation

Evaluates reserve estimates using hindsight analysis, development diagnostics, and reasonableness tests. Ensures reserve selections meet professional and regulatory standards.

Lesson 2 • Loss Development Triangle Analysis

Constructs paid and incurred loss triangles and applies age-to-age factors to project ultimate losses. Establishes the data structure underlying all reserving methods.

Lesson 3 • Expected Loss and Cape Cod Methods

Derives the expected loss method and Cape Cod method as alternatives when data is sparse. Broadens the reserving toolkit for immature or volatile lines.

Lesson 4 • Chain-Ladder and Bornhuetter-Ferguson

Applies the chain-ladder method and the Bornhuetter-Ferguson method to estimate IBNR reserves. Compares the strengths of development-based and a priori loss ratio approaches.

Lesson 1 • Quantitative Risk Measures

Defines Value at Risk, Tail Value at Risk, and coherent risk measures for quantifying loss exposure. Provides the mathematical foundation for capital modelling.

Lesson 2 • Enterprise Risk Management Frameworks

Applies ERM frameworks to identify, assess, and monitor strategic, operational, and financial risks. Integrates quantitative risk measures into organisational governance.

Lesson 3 • Copulas and Dependence Modelling

Models dependence between risk sources using copulas beyond linear correlation. Enables realistic aggregate loss distributions for multi-line insurers.

Lesson 4 • Reinsurance and Risk Transfer

Analyses proportional and non-proportional reinsurance structures and their effect on retained risk. Supports optimal reinsurance purchasing decisions.

Lesson 1 • Predictive Modelling in Actuarial Practice

Applies regression, decision trees, and gradient boosting to actuarial pricing and fraud detection. Extends classical methods with modern machine learning tools.

Lesson 2 • Actuarial Communication and Reporting

Structures actuarial reports, opinions, and presentations for technical and non-technical audiences. Ensures professional standards are met in all deliverables.

Lesson 3 • Strategic Actuarial Leadership

Positions the actuary as a strategic adviser in pricing, capital allocation, and product development decisions. Develops skills to lead cross-functional actuarial initiatives.

Lesson 4 • Pension and Retirement Plan Valuation

Values defined benefit pension obligations using projected unit credit and entry age normal methods. Connects life contingency skills to long-term liability management.