Martingale Theory with Applications, Autumn 2022
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 on teaching weeks. | |
| Support Sessions: | From the second week by Ettore Fincato, see your timetables. | |
| Q&A Session: | Friday 6th January, 11:00am, see Blackboard for Zoom link. Prepare with questions. |
|
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 second 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 26 Sep |
Measure Theory (basic notions, probability) |
1, 2 | -- |
| Thu 29 Sep |
Measure Theory (basic notions, probability) |
3, 4 | -- |
| Fri 30 Sep | Ex. class (sigma-algebras, random variables, stochastic processes, conditional expectation) |
5,
6 |
-- |
| Mon 3 Oct |
Expectation, conditional expectation |
7, 8 | -- |
| Thu 6 Oct | Conditional expectation | 9, 10 |
by noon:
HW1 (sol. on Bb.) |
| Fri 7 Oct | Conditional expectation |
11 |
-- |
| Mon 10 Oct | Conditional expectation | -- | |
| Thu 13 Oct | Probabilistic tools: Borel Cantelli lemmas | 12, 13, 14 | -- |
| Fri 14 Oct | Ex. class (probabilistic tools) | 25, 26, 27, 28 | -- |
| Mon 17 Oct | Probabilistic tools: limits and expectations | 15, 16, 17 | -- |
| Thu 20 Oct | Probabilistic tools: Fubini; inequalities |
18,
19 |
by noon:
HW2 (sol. on Bb.) |
| Fri 21 Oct | Probabilistic tools: inequalities | 20, 21 | -- |
| Mon 24 Oct | Modes of convergence; relations | 22, 23, 24 | -- |
| Thu 27 Oct | Filtrations, Martingales | 29 | -- |
| Fri 28 Oct | Ex. class (martingales: ABRACADABRA) | -- | |
| Mon 31 Oct | Martingales, stopping times | 30, 31, 32 | -- |
| Thu 3 Nov | Random walks and martingales |
by noon:
HW3 (sol. on Bb.) |
|
| Fri 4 Nov | Random walks and martingales | -- | |
| Mon 7 Nov | Upcrossing Lemma, martingale convergence | 33, 34 | -- |
| Thu 10 Nov | Martingale convergence; L2 convergence |
35 |
-- |
| Fri 11 Nov | Ex. class (martingale convergence) | -- | |
| Mon 14 Nov | Doob's decomposition | -- | |
| Thu 17 Nov | Uniform integrability |
by noon:
HW4 (sol. on Bb.) |
|
| Fri 18 Nov | UI and convergence: proofs | 36, 37, 38, 39, 40, 41, 42 | -- |
| Mon 21 Nov | UI martingales | 43, 44 | -- |
| Thu 24 Nov | Tail σ-algebra, 0-1 law; Strong Law of Large Numbers | 45, 46, 47 | -- |
| Fri 25 Nov | Ex. class (Doob's decomp., UI martingales) | -- | |
| Mon 28 Nov | Doob's submartingale inequality | 48 | -- |
| Thu 1 Dec | Doob's submartingale inequality |
by noon:
HW5 (sol. on Bb.) |
|
| Fri 2 Dec | Doob's submartingale inequality: Azuma-Hoeffding | -- | |
| Mon 5 Dec | European option, hedging strategy | 49, 50 | -- |
| Thu 8 Dec | Black-Scholes optional pricing and proof | 51 | -- |
| Fri 9 Dec | Ex. class (Doob submart. ineq., Azuma-Hoeffding) | -- | |
| Mon 12 Dec | Black-Scholes optional pricing proof | 52 | -- |
| Thu 15 Dec | Review |
by noon:
HW6 (sol. on Bb.) |
|
| Fri 16 Dec | Review | -- |
If you have any questions, please contact me (see on top). Click here to see my calendar.
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