Martingale Theory with Applications, Autumn 2021
MATH30027, MATHM0045
This unit will run face-to-face.
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Tel: | +44 (0) 117 4284918 but I'm hardly in the office these days. | |
| Office: | Fry 1.44 | |
| Math cafés: | To be announced soon. | |
| Drop in Sessions: | Wednesdays 13:30 - 14:30 (face-to-face, Fry 1.44) and 18:00 - 19:00 (online, see Zoom link on Blackboard) on teaching weeks. | |
| Nov 10's face-to-face session will be half an hour sooner, 13:00-14:00. | ||
| Extra drop-in session: Tuesday 14th December, 11:00, G.10. | ||
| Support Sessions: | Mondays 16:00 - 17:00 (online with Ziyang Liu, see Zoom link on Blackboard) on weeks 4-6 and 8-12. | |
| Fridays 11:00am - 12:00pm on weeks 3 and 7. | ||
| Q&A Session: | Tuesday 11th January, 3:00pm, 2.41 Fry, and 5pm online (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, except the last week (see below), 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 27 Sep |
Measure Theory (basic notions, probability) |
1, 2 | -- |
| Wed 29 Sep |
Measure Theory (basic notions, probability) |
3, 4 | -- |
| Thu 30 Sep | Ex. class (sigma-algebras, random variables, stochastic processes, conditional expectation) |
5,
6 |
-- |
| Mon 4 Oct |
Expectation, conditional expectation |
7, 8 | -- |
| Wed 6 Oct | Conditional expectation | 9, 10 | -- |
| Thu 7 Oct | Conditional expectation |
11 |
by noon:
HW1 (sol. on Bb.) |
| Mon 11 Oct | Probabilistic tools: Borel Cantelli lemmas | 12, 13, 14 | -- |
| Wed 13 Oct | Probabilistic tools: limits and expectations | 15, 16, 17 | -- |
| Thu 14 Oct | Ex. class (probabilistic tools) | -- | |
| Mon 18 Oct | Probabilistic tools: Fubini; inequalities |
18,
19 |
-- |
| Wed 20 Oct | Probabilistic tools: inequalities | 20, 21 | -- |
| Thu 21 Oct | Modes of convergence | 22, 23 |
by noon:
HW2 (sol. on Bb.) |
| Mon 25 Oct | Modes of convergence: relations | 24 | -- |
| Wed 27 Oct | Modes of convergence: relations and examples; martingales | 25, 26, 27, 28, 29 | -- |
| Thu 28 Oct | Ex. class (martingales) | -- | |
| Mon 1 Nov | Filtrations, martingales | 30, 31 | -- |
| Wed 3 Nov | Optional stopping (ABRACADABRA) | 32 | -- |
| Thu 4 Nov | ABRACADABRA, random walks and martingales |
by noon:
HW3 (sol. on Bb.) |
|
| Mon 8 Nov | Random walks and martingales; Upcrossing Lemma, martingale convergence | 33, 34 | -- |
| Wed 10 Nov | Martingale convergence; L2 convergence |
35 |
-- |
| Thu 11 Nov | Ex. class (martingale convergence) | -- | |
| Mon 15 Nov | Doob's decomposition | -- | |
| Wed 17 Nov | Uniform integrability | 36, 37, 38 | -- |
| Thu 18 Nov | UI and convergence: proofs | 39, 40, 41, 42 |
by noon:
HW4 (sol. on Bb.) |
| Mon 22 Nov | UI martingales | 43, 44 | -- |
| Wed 24 Nov | Tail σ-algebra, 0-1 law; Strong Law of Large Numbers | 45, 46, 47 | -- |
| Thu 25 Nov | Ex. class (Doob's decomp., UI martingales) | -- | |
| Mon 29 Nov | Doob's submartingale inequality | 48 | -- |
| Wed 1 Dec | Doob's submartingale inequality | -- | |
| Thu 2 Dec | Doob's submartingale inequality: Azuma-Hoeffding |
by noon:
HW5 (sol. on Bb.) |
|
| Mon 6 Dec | European option, hedging strategy | 49, 50 | -- |
| Wed 8 Dec | Black-Scholes optional pricing and proof | 51 | -- |
| Thu 9 Dec | Ex. class (Doob submart. ineq., Azuma-Hoeffding) | -- | |
| Mon 13 Dec | Black-Scholes optional pricing proof | 52 | -- |
| Wed 15 Dec | Review |
by noon:
HW6 (sol. on Bb.) |
|
| Thu 16 Dec | Review | -- |
If you have any questions, please contact me (see on top). Click here to see my calendar.
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