Actuarial Mathematics Course

Lesson 1 • Multivariate Probability Concepts

Examines joint, marginal, and conditional distributions for multiple random variables. Supports later modeling of correlated risks and aggregate losses.

Lesson 2 • Probability Theory Essentials

Covers sample spaces, events, conditional probability, and independence. Establishes the probabilistic language used throughout all actuarial models.

Lesson 3 • Time Value of Money

Develops interest accumulation, present value, and discount factors. Forms the financial backbone for pricing and reserving calculations.

Lesson 4 • Random Variables and Distributions

Introduces discrete and continuous random variables and their key distributions. Provides the distributional toolkit underlying loss and survival models.

Lesson 1 • Fractional Age Assumptions

Covers uniform distribution of deaths, constant force, and Balducci assumptions. Enables interpolation of mortality between integer ages.

Lesson 2 • Life Table Construction

Explains the columns of a standard life table and how each is derived. Students learn to build tables from mortality rates and interpret each quantity.

Lesson 3 • Analytical Mortality Laws

Presents parametric mortality models including Gompertz, Makeham, and Weibull laws. Provides closed-form alternatives to tabular mortality data.

Lesson 4 • Select and Ultimate Mortality Tables

Distinguishes select mortality (recently underwritten) from ultimate mortality. Prepares students to use select-and-ultimate tables in insurance pricing.

Lesson 1 • Variable and Increasing Benefits

Values insurance contracts with benefits that change over time. Introduces (IA)x and (DA)x notation for increasing and decreasing benefit structures.

Lesson 2 • Whole Life Insurance Models

Derives the expected present value (APV) of whole life insurance benefits. Connects survival functions and interest theory to produce pricing formulas.

Lesson 3 • Multiple Life Insurance Models

Extends single-life models to joint-life and last-survivor statuses. Enables valuation of products covering two or more lives simultaneously.

Lesson 4 • Multiple Decrement Models

Models competing risks such as death, disability, and withdrawal. Students derive decrements and associated insurance values in a multi-state framework.

Lesson 1 • Whole Life and Temporary Annuities

Derives APVs for whole life and n-year temporary annuities in discrete and continuous forms. Establishes the annuity-insurance relationship central to premium calculation.

Lesson 2 • Annuity Approximations and Woolhouse Formula

Introduces the Woolhouse formula and UDD-based approximations for mthly annuities. Bridges tabular annual data to practical monthly payment calculations.

Lesson 3 • Annuities with Varying Payments

Values annuities with arithmetically or geometrically changing payment amounts. Extends standard annuity models to inflation-adjusted retirement products.

Lesson 4 • Deferred and Certain-and-Life Annuities

Covers annuities with deferred start dates and guaranteed minimum payment periods. Prepares students to price retirement income products with complex structures.

Lesson 1 • Gross Premium Calculation

Incorporates expense loadings into premium calculations to produce gross premiums. Connects theoretical pricing to real-world product development.

Lesson 2 • Premium Variance and Loss Variables

Analyzes the variance of the loss-at-issue variable for various contract types. Supports risk quantification and capital requirement estimation.

Lesson 3 • Special Premium Structures

Examines limited-payment, return-of-premium, and modified premium designs. Prepares students to price non-standard products encountered in practice.

Lesson 4 • Percentile and Portfolio Percentile Premiums

Introduces percentile-based premium principles as alternatives to the equivalence principle. Enables setting premiums that satisfy solvency probability targets.

Lesson 1 • Retrospective Reserve Method

Computes reserves as accumulated past premiums minus accumulated past benefits. Demonstrates equivalence with the prospective method under consistent assumptions.

Lesson 2 • Prospective Reserve Method

Defines the prospective reserve as the APV of future benefits minus future premiums. Derives reserve formulas for whole life, term, and endowment contracts.

Lesson 3 • Modified Reserves

Covers full preliminary term and Commissioner's method reserve modifications. Addresses the new-business strain problem in statutory reserving.

Lesson 4 • Reserves Under Multiple Decrements

Extends reserve calculations to policies with multiple exit causes. Prepares students to value disability, pension, and lapse-sensitive products.

Lesson 1 • Credibility Theory

Applies limited fluctuation and Buhlmann credibility to blend individual and group experience. Supports experience rating and premium adjustment in practice.

Lesson 2 • Risk Measures and Capital Requirements

Defines Value-at-Risk, Tail Value-at-Risk, and related coherent risk measures. Connects loss distributions to regulatory capital and economic capital frameworks.

Lesson 3 • Aggregate Loss Models

Combines frequency and severity models to produce aggregate loss distributions. Enables portfolio-level risk quantification for pricing and capital purposes.

Lesson 4 • Individual Loss Models

Develops models for single-claim severity using parametric distributions. Provides the distributional foundation for pricing and reserving individual policies.

Lesson 1 • Multi-State Markov Models

Generalizes life contingency models to multiple states using Markov chains. Enables valuation of disability, long-term care, and critical illness products.

Lesson 2 • Embedded Options in Insurance Products

Values policyholder options such as guaranteed annuity rates and surrender benefits. Applies option pricing concepts to quantify the cost of contractual guarantees.

Lesson 3 • Stochastic Interest Rate Models

Introduces random interest rate scenarios and their effect on present value distributions. Prepares students to quantify interest rate risk in insurance liabilities.

Lesson 4 • Pension Mathematics and Funding Methods

Applies actuarial methods to defined benefit pension plan valuation and funding. Students compute normal costs and actuarial liabilities under standard funding methods.