Month
|
Day
|
Monday
|
Day
|
Wednesday
|
Day
|
Friday
|
Jan
|
12
|
Lec1:
Introduction:
Course outline; Elements of stochastic
processes: review of basic terminology, two simple examples
|
14
|
Lec2:
Elements of stochastic processes: classification, definition
|
16
|
Lec3:
Markov Chains (MC): examples, transition probabilities
|
Jan
|
19
|
Lec4:
MC:
transition probabilities matrices,
classification of states, recurrence
|
21
|
Lec5:
MCs: basic
limit theorem of Markov chains
|
23
|
Lec6:
MC: finite
state continuous time MC
|
Jan
|
26
|
Lec7:
Renewal
Processes(RP): definition, examples
|
28
|
Lec8: RP: Renewal
Equations
|
30
|
Lec9:
RP:
Renewal Theorems |
Feb
|
2
|
Lec10:
RP: Variations of RP (Delayed, Stationary, CLT,etc.) |
4
|
Lec11:
Martingales: definition, examples, supermartingales and
submartingales (discrete time)
|
6
|
Lec12:
Martingales (sub- and supermartingales): continuous time |
Feb
|
9
|
Lec13: Martingales: The Optional Sampling
Theorem (OST); Applications of OST |
11
|
Lec14:
Martingales: applications to discrete-time (B,S)-security markets
(finance) |
13
|
Lec15:
Brownian Motion (BM): background, joint probabilities |
Feb
|
16
|
Reading Week (No Lectures) |
18
|
Reading Week (No Lectures) |
20
|
Reading Week (No Lectures) |
Feb
|
23
|
Lec16: BM: continuity of paths,
reflection principle and the
maximum value
|
25
|
Lec17: BM: Variations of BM and Extentions
|
27
|
Lec18:
BM: martingale methods |
Mar
|
2
|
Let19: BM: Laplace Transform and
Application in Finance
(Perpetual Warrant)
|
4
|
Lec20:
Miltidimensional BM: Definition, 2-D BM.
|
6
|
Lec21:
Branching Processes
(BP): Examples, pure birth, birth and death processes |
Mar
|
9
|
Lec22: BP: generating function relation
for BP
|
11
|
Lec23:
BP: extinction probabilities, martingale properties
|
13
|
Lec24:
BP: continuous-time,
extinction probabilities
|
Mar
|
16
|
Lec25:
Stationary Processes(SP): definition, examples |
18
|
Lec26:
SP: Mean Square Error Prediction
|
20
|
Lec27:
SP: The Prediction
Theorems and Examples |
Mar
|
23
|
Lec28:
SP: Ergodic Theory
for SP |
25
|
Lec29:
Diffusion Processes (DP): definition, examples |
27
|
Lec30:
DP:
definition,
examples II /Existence and Uniqueness Theorem |
Mar-Apr
|
30
|
Lec31:
DP:
Existence and Uniqueness Theorem /Ito Formula |
1
|
Lec32:
DP: Ito formula /Integration by Parts Formula
|
3
|
Lec33:
DP: Integration by Parts Formula/ Girsanov's Theorem |
Apr
|
6
|
Lec34:
DP: Applications in
Finance, (B,S)-Security Markets, Risk-Neutral Measure
|
8
|
Lec35:
Levy Processes
(LP):
definition, examples, infinite
divisibility |
10
|
Good
Friday (No Lectures) |
Apr
|
13
|
Lec36:
LP: Levy-Khintchine
Formula |
15
|
Lec37:
LP: Poisson Measure and
Integral
|
17
|
Lec38:
LP: Levy-Ito Decomposition/Applications
(finance) |