Actuarial Course

Lesson 1 • Random Variables and Distributions

Defines discrete and continuous random variables and their key distributional properties. Provides the statistical language used throughout all subsequent chapters.

Lesson 2 • Core Probability Concepts

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

Lesson 3 • Essential Mathematical Prerequisites

Reviews calculus, linear algebra, and summation notation required for actuarial models. Ensures all students share a common mathematical baseline.

Lesson 4 • The Actuarial Profession Overview

Covers the scope of actuarial work across industries and the credentialing pathway. Establishes professional context before technical content begins.

Lesson 1 • Common Continuous Distributions

Covers exponential, gamma, Pareto, and lognormal distributions for modelling claim severity. Each distribution's tail behaviour is linked to real insurance loss patterns.

Lesson 2 • Transformations and Mixture Models

Teaches how to derive new distributions via transformations and mixing. Enables modelling of complex, heterogeneous risk populations.

Lesson 3 • Distribution Fitting and Selection

Applies maximum likelihood estimation and goodness-of-fit tests to select distributions. Bridges theoretical distributions to empirical actuarial data.

Lesson 4 • Common Discrete Distributions

Examines Poisson, binomial, and negative binomial distributions used to model claim counts. Connects distributional properties to frequency modelling in non-life insurance.

Lesson 1 • Policy Reserves and Prospective Methods

Calculates prospective and retrospective reserves for life insurance policies. Demonstrates how reserves evolve over the policy term using recursive formulas.

Lesson 2 • Survival Models and Life Tables

Defines the survival function, hazard rate, and curtate future lifetime. Life tables are constructed and interpreted as the basis for all life contingency calculations.

Lesson 3 • Life Insurance Valuation

Calculates actuarial present values for whole life, term, and endowment insurance. Connects mortality probabilities and interest rates to product pricing.

Lesson 4 • Benefit Premiums and Equivalence Principle

Applies the equivalence principle to derive net and gross premiums for life products. Establishes the pricing logic used in all subsequent reserve calculations.

Lesson 1 • Loss Development and Trend Analysis

Applies loss development triangles and trend factors to project ultimate losses. Accurate ultimate loss estimates are essential inputs to the ratemaking formula.

Lesson 2 • Credibility Theory in Ratemaking

Applies limited fluctuation and Bühlmann credibility to blend class and overall experience. Credibility weighting is critical when individual class data are sparse.

Lesson 3 • Ratemaking Fundamentals

Defines the ratemaking process, rate components, and regulatory pricing objectives. Frames the balance between adequacy, equity, and non-excessiveness.

Lesson 4 • Classification Ratemaking

Develops relativities for rating variables using univariate and multivariate techniques. Enables risk segmentation and equitable pricing across policyholder classes.

Lesson 1 • Reserve Uncertainty and Ranges

Quantifies reserve variability using Mack's model and bootstrapping techniques. Provides the statistical basis for reserve ranges and risk capital allocation.

Lesson 2 • Chain-Ladder Development Method

Applies the chain-ladder method to paid and incurred loss triangles. This is the most widely used reserving technique and the benchmark for comparison.

Lesson 3 • Reserving Concepts and Data Structures

Defines IBNR, case reserves, and development triangles as the foundation of reserving. Establishes the data organisation required for all subsequent methods.

Lesson 4 • Cape Cod and Frequency-Severity Methods

Introduces the Cape Cod method and frequency-severity decomposition for reserve estimation. Expands the toolkit for handling unusual loss patterns.

Lesson 1 • Ruin Probability Calculations

Derives exact and approximate formulas for the probability of ultimate ruin. Connects ruin probability to initial surplus and claim severity distribution.

Lesson 2 • Capital Allocation and Risk Aggregation

Applies risk measures to allocate capital across business lines and aggregate correlated risks. Supports enterprise risk management and internal capital modelling.

Lesson 3 • Classical Ruin Theory Framework

Defines the surplus process, premium income, and aggregate claims in the Cramér-Lundberg model. Establishes the mathematical structure for all ruin probability analysis.

Lesson 4 • Reinsurance and Risk Transfer

Evaluates proportional and non-proportional reinsurance structures and their effect on ruin probability. Demonstrates how risk transfer modifies the surplus process.

Lesson 1 • Multiple Decrement Models

Extends single-decrement life tables to model retirement, disability, and death simultaneously. Essential for valuing benefits that depend on competing exit causes.

Lesson 2 • Actuarial Cost Methods

Covers unit credit, projected unit credit, and entry age normal cost methods. Each method allocates pension costs differently over an employee's working life.

Lesson 3 • Actuarial Assumptions for Pensions

Identifies economic and demographic assumptions and their sensitivity impact on liabilities. Proper assumption setting is critical to funding adequacy and financial reporting.

Lesson 4 • Pension Funding and Contribution Requirements

Calculates normal cost, actuarial liability, and unfunded liability for pension plans. Connects valuation results to minimum and maximum contribution requirements.

Lesson 1 • Generalised Linear Models for Actuaries

Applies GLMs with Poisson, gamma, and Tweedie responses to insurance pricing and reserving. Extends classification ratemaking to a rigorous statistical framework.

Lesson 2 • Predictive Analytics and Machine Learning

Applies decision trees, gradient boosting, and neural networks to actuarial classification problems. Evaluates predictive models using actuarial performance metrics.

Lesson 3 • Stochastic Interest Rate Models

Introduces Vasicek, Cox-Ingersoll-Ross, and other term structure models for actuarial use. Enables stochastic valuation of interest-sensitive insurance liabilities.

Lesson 4 • Monte Carlo Simulation in Actuarial Work

Designs and implements Monte Carlo simulations for aggregate loss and reserve distributions. Simulation is the primary tool when closed-form solutions are unavailable.