Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
Printable PDF file
I.
Basic math.
1.
Conditional probability.
2.
Normal distribution.
3.
Brownian motion.
A.
Definition of standard Brownian motion.
B.
Brownian motion passing through gates.
C.
Reflection principle.
D.
Brownian motion hitting a barrier.
4.
Poisson process.
5.
Ito integral.
6.
Ito calculus.
7.
Change of measure.
8.
Girsanov's theorem.
9.
Forward Kolmogorov's equation.
10.
Backward Kolmogorov's equation.
11.
Optimal control, Bellman equation, Dynamic programming.
II.
Pricing and Hedging.
III.
Explicit techniques.
IV.
Data Analysis.
V.
Implementation tools.
VI.
Basic Math II.
VII.
Implementation tools II.
VIII.
Bibliography
Notation.
Index.
Contents.
Brownian motion.
rownian motion arises when the Central Limit Theorem (
CLT
) is applicable to consecutive increments of some stochastic process (see the section (
Why Ito process
)).
The references for this chapter are
[Shreve]
and
[Karatzas1]
.
A.
Definition of standard Brownian motion.
B.
Brownian motion passing through gates.
C.
Reflection principle.
D.
Brownian motion hitting a barrier.
Notation.
Index.
Contents.
Copyright 2007