Sumários

Stochastic interest rates

21 Outubro 2021, 10:30 • João Guerra

Stochastic interest rates. 

Moments of the accumulated value of single investment and of an annual investment when the yields are independent and identically distributed. 
Example. 

Stochastic Differential Equations - Conclusion

19 Outubro 2021, 11:30 • João Guerra

Stochastic differential equations: the Langevin equation and the SDE for the Ornstein-Uhlenbeck process with mean reversion. 

Solutions and distributions of the solutions. 
Applications: the Vasicek model and the stochastic volatility B-S model. 

Stochastic Differential Equations

14 Outubro 2021, 10:30 • João Guerra

Stochastic Differential Equations: motivation. 

Stochastic Differential Equations: Existence and uniqueness of solutions. 
The SDE for geometric Brownian motion. Two methods of solution. 

Itô formula

12 Outubro 2021, 11:30 • João Guerra

Discussion of some exercises on Itô formula.

Multidimensional Itô formula. Examples. 

Itô formula

7 Outubro 2021, 10:30 • João Guerra

Taylor formula and Itô formula. 

Example. 
Itô processes. Definition. 
Itô formula for Itô processes. 
Examples and Exercises.