Quantitative Analysis.

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I. Basic math. 1. Conditional probability. 2. Normal distribution. 3. Brownian motion. 4. Poisson process. 5. Ito integral. 6. Ito calculus. 7. Change of measure. A. Definition of the change of measure. B. Most common application of the change of measure. C. Transformation of SDE under the 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. Bibliography.

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