- Markov Decisions Problems; Bellman’s Equation; Two examples
- A short introduction to Markov chains for dynamic programming
- Definition, Markov Property, some Potential Theory.
- Dynamic Programs; Bellman’s Equation; An example.
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.)
We are interested in solving the constrained optimization problem
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.
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.