Martingale Theory with Applications, Autumn 2023
MATH30027, MATHM0045
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Tel: | +44 (0) 117 4557958 | |
| Office: | Fry 1.44 | |
| Drop in Sessions: | Wednesdays 13:30 - 14:30, 1.44 Fry in teaching weeks, except Week 1. | |
| Weds 25th October, 15th November and 6th December it's from 13:00-13:55. |
|
Below is a detailed schedule. Topics of future events are plans, and can change. Topics of past events serve as log.
Homeworks are/will also be posted here: just click those with a link below. They are due every third Thursday at 12:00pm in Blackboard.
Homework solutions will appear on Blackboard, please email me if you have problem accessing these.
| Date | Topics | Past videos | Homework due: |
|---|---|---|---|
| Mon 25 Sep |
Measure Theory (basic notions, probability) |
1, 2 | -- |
| Tue 26 Sep |
Measure Theory (basic notions, probability) |
3, 4 | -- |
| Wed 27 Sep | Ex. class (sigma-algebras, random variables, stochastic processes, conditional expectation) |
5,
6 |
-- |
| Mon 2 Oct |
Expectation |
7, 8 | -- |
| Tue 3 Oct | Conditional expectation | 9, 10 | -- |
| Wed 4 Oct | Conditional expectation |
11 |
-- |
| Mon 9 Oct | Conditional expectation | -- | |
| Tue 10 Oct | Probabilistic tools: Borel Cantelli lemmas | 12, 13, 14 | -- |
| Wed 11 Oct | Ex. class (probabilistic tools) | 25, 26, 27, 28 | -- |
|
by noon Thu 12 Oct:
HW1 (sol. on Bb.) |
|||
| Mon 16 Oct | Probabilistic tools: limits and expectations | 15 | -- |
| Tue 17 Oct | Probabilistic tools: limits and expectations | 16, 17 | -- |
| Wed 18 Oct | Probabilistic tools: Fubini; inequalities | 18, 19 | -- |
| Mon 23 Oct | Inequalities; modes of convergence: relations | 20, 21, 22, 23, 24 | -- |
| Tue 24 Oct | modes of convergence: relations; filtrations, martingales | 29 | -- |
| Wed 25 Oct | Ex. class (martingales: ABRACADABRA) | -- | |
| Mon 30 Oct | Martingales, stopping times | 30, 31, 32 | -- |
| Tue 31 Oct | Optional stopping, stopping times | -- | |
| Wed 1 Nov | Random walks and martingales | -- | |
|
by noon Thu 2 Nov:
HW2 (sol. on Bb.) |
|||
| Mon 6 Nov | Upcrossing Lemma, martingale convergence | 33, 34 | -- |
| Tue 7 Nov | Martingale convergence; L2 convergence |
35 |
-- |
| Wed 8 Nov | Ex. class (martingale convergence) | -- | |
| Mon 13 Nov | Doob's decomposition | -- | |
| Tue 14 Nov | Uniform integrability | -- | |
| Wed 15 Nov | UI and convergence: proofs | 36, 37, 38, 39, 40, 41, 42 | -- |
| Mon 20 Nov | UI martingales | 43, 44 | -- |
| Tue 21 Nov | Tail σ-algebra, 0-1 law | 45 | -- |
| Wed 22 Nov | Strong Law of Large Numbers; Ex. class (Doob's decomp., UI martingales) | 46, 47 | -- |
|
by noon Thu 23 Nov:
HW3 (sol. on Bb.) |
|||
| Mon 27 Nov | Doob's submartingale inequality (and Ex. class) | 48 | -- |
| Tue 28 Nov | Doob's submartingale inequality | -- | |
| Wed 29 Nov | Doob's submartingale inequality: Azuma-Hoeffding | -- | |
| Mon 4 Dec | Azuma-Hoeffding; examples | -- | |
| Tue 5 Dec | European option, hedging strategy; Black-Scholes optional pricing and proof | 49, 50, 51 | -- |
| Wed 6 Dec | Black-Scholes optional pricing proof | 52 | -- |
| Mon 11 Dec | Ex. class (Azuma-Hoeffding) | -- | |
| Tue 12 Dec | Black-Scholes optional pricing proof | -- | |
| Wed 13 Dec | Review | -- | |
|
by noon Thu 14 Dec:
HW4 (sol. on Bb.) |
If you have any questions, please contact me (see on top). Click here to see my calendar.
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