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Probability and Stochastics for Finance

Probability and Stochastics for Finance. Instructor: Dr. Joydeep Dutta, Department of Humanities and Social Sciences, IIT Kanpur. This course provides the minimum mathematical requirements to study mathematical finance or more precisely the pricing of financial derivatives. Topics covered in the lectures include: basic probability, random variables, distribution function and independence, Chebyshev inequality, Borel-Cantelli lemma, law of large numbers and central limit theorem, conditional expectation, martingales, Brownian motion, stochastic integrals, Ito calculus, and stochastic differential equations. (from nptel.ac.in)

Basic Probability


Lecture 01 - Basic Probability
Lecture 02 - Interesting Problems in Probability
Lecture 03 - Random Variables, Distribution Function and Independence
Lecture 04 - Chebyshev Inequality, Borel-Cantelli Lemma and Related Issues
Lecture 05 - Law of Large Number and Central Limit Theorem
Lecture 06 - Conditional Expectation
Lecture 07 - Conditional Expectation (cont.)
Lecture 08 - Martingales
Lecture 09 - Brownian Motion I
Lecture 10 - Brownian Motion II
Lecture 11 - Brownian Motion III
Lecture 12 - Ito Integral
Lecture 13 - Ito Integral (cont.)
Lecture 14 - Ito Calculus
Lecture 15 - Ito Calculus (cont.)
Lecture 16 - Ito Integral in Higher Dimension
Lecture 17 - Application of Ito Integrals
Lecture 18 - Application of Ito Integrals (cont.)
Lecture 19 - Black-Scholes Formula
Lecture 20 - Black-Scholes Formula (cont.)

References
Probability and Stochastics for Finance
Instructor: Dr. Joydeep Dutta, Department of Humanities and Social Sciences, IIT Kanpur. This course provides the minimum mathematical requirements to study mathematical finance or more precisely the pricing of financial derivatives.