Objectives

The Itô's calculus, introduced in 1944 by K. Itô, and the martingale theory constitute the mathematical basis to model the price of stocks, analyze the price of options in complete and incomplete markets as well to maximize the utility function of investors Consumers.

Program

1. Stochastic integrals
2. Itô's formula
3. Girsanov's Theorem
4. Stochastic Differential Equations
5. Diffusion Processes
6. Application to Finance (Black-Scholes Model)

Bibliography

• Durret, R. Stochastic Calculus: A Practical Introduction. CRC Press, 1996.
• Karatzas, I. and  Shreve, S., Brownian Motion and Stochastic Calculus, Second Edition. Springer Verlag, 1991.
• Oksendal,  B., Stochastic Differential Equations.  Springer, 1998