Martingale Theory with Applications, Autumn 2024
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 Thursdays on Weeks 3, 6, 9, 11 (not 12!) 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 17 Sep |
Measure Theory (basic notions, probability) (first year version) |
1, 2 | -- |
| Wed 18 Sep |
Measure Theory (basic notions, probability) (first year version) |
3, 4 | -- |
| Thu 19 Sep | Sigma-algebras, random variables, stochastic processes, expectation |
5,
6 |
-- |
| Tue 24 Sep |
Expectation, conditional expectation |
7, 8 | -- |
| Wed 25 Sep | Conditional expectation | 9, 10 | -- |
| Thu 26 Sep | Conditional expectation |
11 |
-- |
| Tue 1 Oct | Conditional expectation | -- | |
| Wed 2 Oct | Probabilistic tools: Borel Cantelli lemmas | 12, 13, 14 | -- |
| Thu 3 Oct | Probabilistic tools: limits and expectations | 15, 16 |
by noon:
HW1 (sol. on Bb.) |
| Tue 8 Oct | Probabilistic tools: limits and expectations | 17 | -- |
| Wed 9 Oct | Probabilistic tools: Fubini; inequalities | 18, 19 | -- |
| Thu 10 Oct | Inequalities; modes of convergence | 20, 21, 22 | -- |
| Tue 15 Oct | Modes of convergence: relations | 23, 24 | -- |
| Wed 16 Oct | Filtrations, martingales | 25, 26, 27 | -- |
| Thu 17 Oct | Stopping times, optional stopping | 28 | -- |
| Tue 22 Oct | Ex. class (probabilistic tools) | 29, 30, 31, 32 | -- |
| Wed 23 Oct | Ex. class (martingales: ABRACADABRA) | -- | |
| Thu 24 Oct | Ex. class (random walks and martingales) |
by noon:
HW2 (sol. on Bb.) |
|
| Tue 29 Oct | Upcrossing Lemma, martingale convergence | 33, 34 | -- |
| Wed 30 Oct | Martingale convergence | -- | |
| Thu 31 Oct | L2 convergence; Doob's decomposition |
35 |
-- |
| Tue 5 Nov | Doob's decomposition | -- | |
| Wed 6 Nov | Uniform integrability | 36, 37 | -- |
| Thu 7 Nov | UI and convergence: proofs | 38, 39, 40, 41, 42 | -- |
| Tue 12 Nov | UI martingales; tail σ-algebra | 43, 44 | -- |
| Wed 13 Nov | 0-1 law; Strong Law of Large Numbers | 45, 46, 47 | -- |
| Thu 14 Nov | Doob's submartingale inequality | 48 |
by noon:
HW3 (sol. on Bb.) |
| Tue 19 Nov | Doob's submartingale inequality | -- | |
| Wed 20 Nov | Azuma-Hoeffding concentration | -- | |
| Thu 21 Nov | Azuma-Hoeffding concentration | -- | |
| Tue 26 Nov | European option, hedging strategy; Black-Scholes optional pricing and proof | 49, 50, 51 | -- |
| Wed 27 Nov | Black-Scholes optional pricing proof | 52 | -- |
| Thu 28 Nov | Black-Scholes optional pricing proof |
by noon:
HW4 |
|
| Tue 3 Dec | Ex. class (Doob's decomposition, martingale convergence, UI martingales) | -- | |
| Wed 4 Dec | Ex. class (Azuma-Hoeffding) | -- | |
| Thu 5 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.
To the teaching page