Actuarial Mathematics
The core mathematics of the actuarial profession: interest theory, life contingencies, loss models, credibility and ratemaking, plus how to plan the SOA and CAS exams.
Leads to: Actuary
Before you start
This course builds on Probability & Statistical Inference, Calculus & Linear Algebra for STEM and Spreadsheets for Data Work. Take them first if you are new to the topic.
About this course
This mid-level course is for learners heading toward a career as an actuary. It builds on Probability & Statistical Inference, Calculus & Linear Algebra and Spreadsheets for Data Work, and turns those tools into the methods actuaries use every day. The first module covers financial mathematics: present values, annuities and loan amortization, and bond pricing with duration, the material of the SOA/CAS Exam FM. The second module introduces life contingencies: survival probabilities from a life table, actuarial present values of life insurance and annuities, net premiums and why insurers hold reserves. The third module turns to property and casualty work: aggregate loss models built from frequency and severity, credibility theory for blending a group's experience with a manual rate, and a loss ratio rate indication written in SQL. The last module is about becoming an actuary: the SOA and CAS exam paths with a dated study plan for Exam P or FM, a chain ladder reserving triangle built in a spreadsheet, and the profession's Code of Professional Conduct and Actuarial Standards of Practice. Seven lessons end with a Python exercise you run in your browser, and examples use small, made-up data. The course does not replace the professional exams: becoming a credentialed actuary requires passing the SOA or CAS exam series and meeting their education and experience requirements, which are linked from the lessons.
Course content
Module 1
Financial Mathematics
3 lessons · 1h 47mPrice cash flows with the time value of money, value annuities and loans, and measure a bond's price and interest-rate risk.
- 29mTime value of moneyReading
Price any set of future cash flows by discounting them to today with an interest rate.
- 41mAnnuities and loansReading
Value a level series of payments and build the amortization schedule for a loan.
- 37mBonds and yieldReading
Price a fixed-coupon bond from its yield and measure its interest-rate risk with duration.
Module 2
Life Contingencies
3 lessons · 1h 52mRead life tables, price life insurance and annuities with actuarial present values, and understand why insurers hold reserves.
- 38mSurvival models and life tablesReading
Read a life table and turn it into survival and death probabilities for any age and period.
- 32mLife insurance and annuity valuesReading
Combine discounting with survival probabilities to price a term insurance policy with level premiums.
- 42mReservesReading
Understand why insurers hold policy reserves and how a prospective reserve is calculated.
Module 3
Risk and Loss Models
3 lessons · 1h 55mModel aggregate losses from frequency and severity, blend experience with credibility, and compute an indicated rate change.
- 40mFrequency and severityReading
Model total annual losses as a random number of claims with random sizes, by formula and by simulation.
- 33mCredibilityReading
Decide how much to trust a group's own claims experience and blend it with a manual rate.
- 42mRatemaking basicsReading
Use the loss ratio method to compute an indicated rate change from premium and loss data.
Module 4
Exams and Practice
3 lessons · 1h 55mPlan the SOA and CAS exam path, build a reserving triangle in a spreadsheet, and apply the profession's code and standards.
- 39mSOA and CAS exam pathsReading
Understand how actuaries qualify through SOA or CAS exams and build a realistic study plan for Exam P and FM.
- 53mActuarial work in spreadsheetsReading
Build a loss development triangle and a chain ladder reserve estimate in a spreadsheet.
- 23mActuarial professionalismReading
Apply the Code of Professional Conduct and the Actuarial Standards of Practice to realistic workplace cases.