Martingale Theory with Applications, Autumn 2025
MATH30027, MATHM0045
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Tel: | +44 (0) 117 4557958 | |
| Office: | Fry 1.44 | |
| Drop in Sessions: | Wednesdays 16:30 - 17:30, 1.44 Fry in teaching weeks. |
|
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 on each Thursday of Weeks 3-5 and 7-11 at noon in Blackboard.
Homework solutions will appear on Blackboard, please email me if you have problem accessing these.
| Date | Topics | Past videos | Homework due: |
|---|---|---|---|
| Tue 23 Sep |
Measure Theory (basic notions, probability) (first year version) |
1, 2 | -- |
| Wed 24 Sep |
Measure Theory (basic notions, probability) (first year version) |
3, 4 | -- |
| Thu 25 Sep | Sigma-algebras, random variables, stochastic processes, expectation |
5,
6 |
-- |
| Tue 30 Sep |
Expectation, conditional expectation |
7, 8 | -- |
| Wed 1 Oct | Conditional expectation | 9, 10 | -- |
| Thu 2 Oct | Conditional expectation |
11 |
-- |
| Tue 7 Oct | Conditional expectation | -- | |
| Wed 8 Oct | Probabilistic tools: Borel Cantelli lemmas | 12, 13, 14 | -- |
| Thu 9 Oct | Probabilistic tools: limits and expectations | 15, 16 |
by noon:
HW1 |
| Tue 14 Oct | Probabilistic tools: limits and expectations | 17 | -- |
| Wed 15 Oct | Probabilistic tools: Fubini; inequalities | 18, 19 | -- |
| Thu 16 Oct | Inequalities; modes of convergence | 20, 21, 22 |
by noon:
HW2 |
| Tue 21 Oct | Modes of convergence: relations | 23, 24 | -- |
| Wed 22 Oct | Filtrations, martingales | 25, 26, 27 | -- |
| Thu 23 Oct | Stopping times, optional stopping | 28 |
by noon:
HW3 |
| Tue 28 Oct | Ex. class (probabilistic tools) | 29, 30, 31, 32 | -- |
| Wed 29 Oct | Ex. class (martingales: ABRACADABRA) | -- | |
| Thu 30 Oct | Ex. class (random walks and martingales) | -- | |
| Tue 4 Nov | Upcrossing Lemma, martingale convergence | 33, 34 | -- |
| Wed 5 Nov | Martingale convergence | -- | |
| Thu 6 Nov | L2 convergence; Doob's decomposition |
35 |
by noon:
HW4 |
| Tue 11 Nov | Doob's decomposition | -- | |
| Wed 12 Nov | Uniform integrability | 36, 37 | -- |
| Thu 13 Nov | UI and convergence: proofs | 38, 39, 40, 41, 42 |
by noon:
HW5 |
| Tue 18 Nov | UI martingales; tail σ-algebra | 43, 44 | -- |
| Wed 19 Nov | 0-1 law; Strong Law of Large Numbers | 45, 46, 47 | -- |
| Thu 20 Nov | Doob's submartingale inequality | 48 |
by noon:
HW6 |
| Tue 25 Nov | Doob's submartingale inequality | -- | |
| Wed 26 Nov | Azuma-Hoeffding concentration | -- | |
| Thu 27 Nov | Azuma-Hoeffding concentration |
by noon:
HW7 |
|
| Tue 2 Dec | European option, hedging strategy; Black-Scholes optional pricing and proof | 49, 50, 51 | -- |
| Wed 3 Dec | Black-Scholes optional pricing proof | 52 | -- |
| Thu 4 Dec | Black-Scholes optional pricing proof |
by noon:
HW8 |
|
| Tue 9 Dec | Ex. class (Martingale convergence, UI martingales) | -- | |
| Wed 10 Dec | Ex. class (Azuma-Hoeffding) | -- | |
| Thu 11 Dec | Review | -- |
If you have any questions, please contact me (see on top). Click here to book a meeting with me if the drop-in sessions don't work for you for some reason.
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