Week 01

Lecture: [1]

Class: First step analysis, expected time to get HTH.

Week 02

Lecture: [2]

Class: Markov chain states classification

Week 03

Lecture: [3]

Class: Poisson process.

Week 04

Lecture: [4]

Class: Conditional expected value. Conditional variance.

Week 05

Lecture: [5]

Class: Sigma-algebras, measurability. Conditional expected value with respect to sigma-algebra.

Week 06

Lecture:

Class: Probability limit, Moment generating function

Midterm

The long-awaited midterm will be on 28 October, 10:00 - 12:00.

Duration: 120 minutes. No proctoring.

Topics:

• First step analysis
• Classification of states and classes of MC.
• Conditional expected value (two views).
• Poisson process.
• Sigma algebras.
• Probability limit
• Moment generating function

Week

Date: 2021-10-28

Lecture:

Class: Martingales in discrete time

Week

Date: 2021-11-09

Lecture:

Class: Wiener process definition, basic properties, inversion

Week

Date: 2021-11-16

Lecture:

Class: Stochastic integral, intuition, limit in L2

Week

Date: 2021-11-23

Lecture:

Class: Stochastic integral properties, Ito's lemma

Week

Date: 2021-11-30

Lecture:

Class: BS model, Girsanov theorem, pricing

Week

Date: 2021-12-07

Lecture:

Class: more pricing examples in BS model

Week

Date: 2021-12-14

Lecture:

Class: Recap on martingales, Ito, etc