Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
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I. Basic math.
1. Conditional probability.
A. Definition of conditional probability.
B. A bomb on a plane.
C. Dealing a pair in the "hold' em" poker.
D. Monty-Hall problem.
E. Two headed coin drawn from a bin of fair coins.
F. Randomly unfair coin.
G. Recursive Bayesian calculation.
H. Birthday problem.
I. Backward induction.
J. Conditional expectation. Filtration. Flow of information. Stopping time.
2. Normal distribution.
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.

Birthday problem.


here are $N$ people in the room. What is the probability that at least two of them have the same birthday?

Set $M=365.$ We are interested in MATH we fix a person A, MATH by the formula ( Bayes formula ) MATH MATH MATH where $\frac{1}{M}$ is the probability that a particular person has the same birthday as A, $1-\frac{1}{M}$ is the probability that a particular person does not have the same birthday as A, MATH is the probability that in a group of $N-1$ randomly selected individuals no one has the same birthday as A and MATH is the probability that in a group of $N-1$ randomly selected individuals someone has the same birthday as A.





Notation. Index. Contents.


















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