Content of present website is being moved to www.lukoe.com/finance . Registration of www.opentradingsystem.com will be discontinued on 2020-08-14.
Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
Printable PDF file
I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
1. Finite differences.
2. Gauss-Hermite Integration.
3. Asymptotic expansions.
4. Monte-Carlo.
A. Generation of random samples.
a. Uniform [0,1] random variable.
b. Inverting cumulative distribution.
c. Accept/reject procedure.
d. Normal distribution. Box-Muller procedure.
e. Gibbs sampler.
B. Acceleration of convergence.
C. Longstaff-Schwartz technique.
D. Calculation of sensitivities.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Inverting cumulative distribution.


laim

Suppose a random variable $X$ is given by a distribution density function $p\left( x\right) $ : MATH Let $F\left( x\right) $ be the cumulative distribution of $X$ : MATH The MATH is the inverse function of $F$ : MATH . The variable MATH has the same distribution as $X$ .

Proof

Indeed, MATH MATH MATH





Notation. Index. Contents.


















Copyright 2007