Month

Day

Wednesday

Day

Friday

Day

Monday

Jan

9

Lec1: Intro to Stochastic Processes
I

11

Lec2: Intro to Stochastic Processes II

14

Lec3: Brownian Motion (BM)

Jan

16

Lec4: BM: Continuity of Path, Maximum
Value, Arccos Law

18

Lec5: Variations of BM and Extensions

21

Lec6: Some Functionals of BM by
Martingale Methods

Jan

23

Lec7: Applications of BM in Finance

25

Lec8: Brownian Bridge

28

Lec9: Multidimensional BM 
JanFeb

30

Lec10: Gaussian Processes

1

Lec11: Fractional BM and OU Process 
4

Lec12: Martingales: Discrete Time 
Feb

6

Lec 13: Martingales: Continuous Time

8

Lec14: Stopping Times, Optional Stopping
Theorem, Wald's Identities

11

Lec15: Martingales in Finance (Discrete
Time): (B,S)security MarketMain Definitions 
Feb

13

Lec16: Martingales in Finance
(Discrete Time): (B,S)security MarketOptions 
15

Lec17: Markov Processes (MP) 
18

Reading
Week (No Lectures): Feb 1824
Monday, Jan 25: Lec 18: Semigroups and
their Generators for MP

FebMar

27

Lec19: Diffusion Processes
(DP): Ito Integral

1

Lec20: SDEs: GBM, OU & Vasicek
Processes 
4

Lec21:
General SDEs 
Mar

6

Lec22: Ito and Other Formulas 
8

Lec23: Absolute Continuity and the
RadonNikodym Theorem 
11

Lec24: Girsanov's Theorem and
RiskNeutral Measure 
Mar

13

Lec25:
Continuoustime (B,S)security market (Basics)

15

Lec26: Levy
Processes (LP) as MP

18

Lec27: The
LevyKhintchine Formula

Mar

20

Lec28: Properties of LP 
22

Lec29: The LevyIto Decomposition

25

Lec30: Semigroups and
Generators of LP 
MarApr

27

Lec31:
Semigroups and Generators of LP II

29

Good Friday (No
Lecture) 
1

Lec32:
Martingale Problem for MP 
Apr

3

Lec33: Martingale Problem for
MP II

5

Lec34: Markov
Chains (MC) 
8

Lec35: Martingale Problem for
MC 
Apr

10

Lec36: Martingale Problem for DP 
12

Lec37: Martingale Problem for
a General MP 
15

Lec38: History,
Ideas, Applications of Levy processesone of the most
amazing Markov processes.
