Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
1. Conditional probability.
2. Normal distribution.
A. Definition of normal variable.
B. Linear transformation of random variables.
C. Multivariate normal distribution. Choleski decomposition.
D. Calculus of normal variables.
E. Central limit theorem (CLT).
3. Brownian motion.
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.

Definition of normal variable.

he normal random variable, denoted MATH , is described by the distribution density MATH MATH the $\mu$ and $\sigma$ are real numbers.

The notation $\xi$ is generally reserved for MATH

MATH (Standard normal variable)
MATH is called "the standard normal variable".

Notation. Index. Contents.

Copyright 2007