Course

FIN-415: Probability and stochastic calculus

Summary

This course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. The fundamental notions and techniques introduced in this course have many applications in finance, for example for option pricing, risk management and optimal portfolio choice.

Lectures

Instructor

Elena Perazzi

Teaching & PhD Courses Advanced derivatives FIN-503 The course covers a wide range of advanced topics in derivatives pricing Game theory and strategic decisions MGT-300 Game theory studies the strategic interactions between rational agents. It has a myriad of applications in politics, business, sports. A special branch of Game Theory, Auction Theory, has recently guided the development of Ebay, Google advertising auctions, and of the Wireless spectrum auctions. Probabili

Official source

https://edu.epfl.ch/coursebook/en/probability-and-stochastic-calculus-FIN-415

Moodle Page

http://go.epfl.ch/FIN-415

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Summary

Lectures

Instructor

Elena Perazzi

Official source

https://edu.epfl.ch/coursebook/en/probability-and-stochastic-calculus-FIN-415

Moodle Page

http://go.epfl.ch/FIN-415

About this result

Lectures in this course (14)

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Differential Equations: Examples and Relations

Explores Stochastic Differential Equations with examples like Brownian Motion and Square-Root Processes, discussing their relation to Partial Differential Equations.

Girsanov's Theorem: Numerical Simulation of SDEs

Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.

Numerical Simulation of SDEs: Monte Carlo & Optimal Control

Covers Monte Carlo methods, variance reduction, and stochastic optimal control, exploring simulation techniques, efficiency, and investment dynamics.

Stochastic Optimal Control: Martingale Theorem

Explores Stochastic Optimal Control, emphasizing Optimal Consumption and Investment, the Martingale Representation Theorem, and the Verification Theorem.

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