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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.

Accept/reject procedure.


laim

The variables $X$ and $Y$ are given by the distributions MATH and MATH with common support. Assume that MATH We generate the variable $X$ as follows:

Step 1. Generate $\eta$ and $Y$ independently.

Step 2. If MATH then set $X=Y$ otherwise return to step 1.

Proof

Indeed, MATH MATH MATH MATH It is a part of the above computation that MATH Hence, for the procedure to be effective, $M$ has to be large.





Notation. Index. Contents.


















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