- A short introduction to Markov chains for dynamic programming
- Definition, Markov Property, some Potential Theory.
Dynamic Programming
Finance for Actuarial
A summary of Finance for Actuarial course:
- Cash Flows; Time & Rounding Conventions; Glossary of (some) Financial Products
- Simple & compound interest; Rate of Discount; Nominal Interest; Accumulation Factors; Force of Interest
- Discounted, Accumulate & Present Value; Continuous Cash flows.
- Annuties Immediate & Due; present and future values; increasing & perpetuities…
- Loan schedules; Level Installments; APR and Flat rate
- Equations of Value and Yield.
(This covers about half of the Institute and Faculty of Actuaries CT1 exam — though you should probably work on context if you want to pass the exam.)
Lagrangian Optimization
We are interested in solving the constrained optimization problem

Talagrand’s Concentration Inequality
We prove a powerful inequality which provides very tight gaussian tail bounds “” for probabilities on product state spaces
. Talagrand’s Inequality has found lots of applications in probability and combinatorial optimization and, if one can apply it, it generally outperforms inequalities like Azzuma-Hoeffding.
Lecture 0. Some Basic Maths for Actuarial Students
We will regularly need to employ certain calculations. In MATH10951 the context might vary but the maths varies much less. These notes are more of a background check on prequisties. We cover
- Power, the exponential, logarithms, the (natural) logarithm.
- Arithmetic and Geometric progressions.
Continue reading “Lecture 0. Some Basic Maths for Actuarial Students”
Markov Chains: a functional view
- Laplacian; Adjoints; Harmonic fn; Green’s fn; Forward Eqn; Backward Eqn.
- Markov Chains and Martingales; Green’s Functions and occupancy; Potential functions; time-reversal and adjoints.
Spitzer’s Lyapunov Ergodicity
We show that relative entropy decreases for continuous time Markov chains.
Sums and Limits of Coin Throws
We explain why certain distributions arise naturally as the limit of coin throws.
- Bernoulli, Binomial Distributions, Geometric Distributions.
- Binomial to Poisson Distribution; Geometric to Exponential; Binomial to Normal.
A Mean Field Limit
We consider a system consisting of interacting objects. As we let the number of objects increase, we can characterize the limiting behaviour of the system.