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8181: Advanced Topics in Microeconomics

Stochastic calculus and applications to dynamic programming and finance

Aim: We provide the basic notions of stochastic calculus. This is a course to provide technical skills. It should be of interest to people aiming at research in Micro Theory, Game Theory, Finance, dynamic macroeconomics.

Syllabus:

Week

Content

1

Preliminaries and Brownian Motion

2

Ito Integral

3

Ito' formula and martingale representation theorem

4

Stochastic Differential equations

5

Diffusions and Markov processes

6

Kolmogorov's equations and Girsanov's theorem

7

Dynamic programming in Continuous time

8

Applications to finance

 Textbooks:



1

Oksendal, Stochastic Differential Equations

Springer

2

Karatzas Shreve, Brownian Motion and Stochastic Calculus

Springer



  


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