MAST 729
Selected Topics in Actuarial Mathematics
Fall 2026 · Selected Topics in Probability, Statistics and Actuarial Mathematics
Topics
- Discrete-time option pricing and model calibration
- Implied-volatility trees
- Probability, Brownian motion and stochastic calculus
- Continuous-time financial models and risk-neutral hedging
- Monte Carlo simulation and SDE discretization
- Variance reduction
- Volatility estimation and volatility surfaces
- Stochastic interest rates and term-structure models
- PDE valuation and finite-difference methods
- American and path-dependent claims
- Risk measures, Greeks and model risk
Readings
- Self-contained lecture notes, slides and exercises.
Fall 2026 · Topics in Statistics
Topics
- Multi-armed bandit problems
- Markov decision problems
- Dynamic programming
- Tabular Monte Carlo and temporal-difference methods
- Policy gradients
- Approximation methods
- Deep reinforcement learning
- Reinforcement-learning programming in R
Readings
- Miguel Morales. Grokking Deep Reinforcement Learning. Manning.
- Listed textbook (requirement not stated): R. S. Sutton and A. G. Barto. Reinforcement Learning: An Introduction, 2nd edition. MIT Press. http://incompleteideas.net/book/the-book-2nd.html
Fall 2026 · STAT 497
Readings
- Reinforcement Learning: An Introduction, by R.S. Sutton and A.G. Barto, 2nd Edition, MIT Press.
Winter 2026 · Selected Topics in Probability, Statistics and Actuarial Mathematics
Topics
- One- and multi-period binomial no-arbitrage pricing
- State prices, changes of measure and Radon–Nikodym derivatives
- CAPM, utility maximization and optimal investment
- European, American and exotic derivatives
- Stopping times
- Interest-rate binomial models and bond derivatives
- Forward measure, Ho–Lee and Black–Derman–Toy models
- Forward and futures contracts
Readings
- Steven Shreve. Stochastic Calculus for Finance I: The Binomial Asset Pricing Model. Springer, 2005.
- Self-contained lecture slides.
Winter 2026 · Statistical Simulation
Topics
- Probability review and random-number generation
- Generating discrete and continuous random variables
- Discrete-event simulation
- Statistical analysis of simulated data
- Monte Carlo estimation
- Variance-reduction methods
- Simulation of stochastic systems
Readings
- Listed textbook (requirement not stated): Sheldon M. Ross. Simulation, 6th edition. Academic Press.
Winter 2025 · STAT 461
Readings
- Simulation, 5th Edition, by Sheldon M. Ross (Academic Press).
Winter 2024 · STAT 461
Readings
- Simulation, 5th Edition, by Sheldon M. Ross (Academic Press).
Fall 2023 · ACTU 491
Readings
- I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer.
- B. Oksendal, Stochastic Differential Equations, Springer.
Fall 2023 · MACF 491
Readings
- I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer.
- B. Oksendal, Stochastic Differential Equations, Springer.
Winter 2023 · STAT 461
Readings
- Sheldon M. Ross, Simulation, 5th edition, Academic Press; 6th edition also available as a reference.
Winter 2022 · ACTU 491
Readings
- I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer.
- B. Oksendal, Stochastic Differential Equations, Springer.
Winter 2022 · MACF 491
Readings
- I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer.
- B. Oksendal, Stochastic Differential Equations, Springer.
Winter 2022 · STAT 461
Readings
- Simulation, 5th Edition, by Sheldon M. Ross (Academic Press).
Fall 2021 · ACTU 491
Readings
- Shapiro, A., Dentcheva, D., & Ruszczyński, A. (2014). Lectures on stochastic programming: modeling and theory. Society for Industrial and Applied Mathematics.
- Marceau, É. (2013). Modélisation et évaluation quantitative des risques en actuariat, Modèle sur une période, Springer-Verlag, France.
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Fall 2026
- Syllabus or course outline ↗Fall 2026
- Historical course outline ↗Fall 2026
- Syllabus or course outline ↗Winter 2026
- Syllabus or course outline ↗Winter 2026
- Historical course outline ↗Winter 2025
- Historical course outline ↗Winter 2025
- Historical course outline ↗Winter 2024
- Historical course outline ↗Winter 2024
- Historical course outline ↗Fall 2023
- Historical course outline ↗Fall 2023
- Historical course outline ↗Winter 2023
- Historical course outline ↗Winter 2023
- Historical course outline ↗Winter 2022
- Historical course outline ↗Winter 2022
- Historical course outline ↗Winter 2022
- Historical course outline ↗Winter 2022
- Historical course outline ↗Fall 2021
- Fall 2026 outline. Course header explicitly lists MACF 402, MAST 729, MAST 881. Explicitly no required text. Recommended reference texts are listed on Moodle, but their bibliographic details are not public in this outline.
- Fall 2026 outline. Course header explicitly lists MACF 491, STAT 497, MAST 679, MAST 729, MAST 881. Morales is explicitly an optional reference. The first-page header includes MAST 729, although subsequent footers omit that code.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Winter 2026 outline. Course header explicitly lists MACF 401, MAST 729, MAST 881. The content is based on Shreve, but purchasing the book is explicitly optional because the slides are self-contained.
- Winter 2026 outline. Course header explicitly lists STAT 461, MAST 729, MAST 881.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.