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.)
Continue reading “Finance for Actuarial”
We are interested in solving the constrained optimization problem
Continue reading “Lagrangian Optimization”
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.
Continue reading “Talagrand’s Concentration Inequality”
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”
- 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.
Continue reading “Markov Chains: a functional view”
We show that relative entropy decreases for continuous time Markov chains.
Continue reading “Spitzer’s Lyapunov Ergodicity”
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.
Continue reading “Sums and Limits of Coin Throws”