3. Stochastic Calculus

Stochastic Integral — Quiz

Test your understanding of stochastic integral with 5 practice questions.

Practice Questions

Question 1

Which of the following conditions is required for a process $H_t$ to be an admissible integrand in the construction of the Itô integral?

Question 2

The Itô integral is defined for integrands that are adapted and square-integrable. What does 'adapted' mean in the context of a stochastic process $H_t$ with respect to a filtration $\mathcal{F}_t$?

Question 3

Which of the following statements correctly describes the Itô isometry for a simple predictable process $H_s$ and a Brownian motion $B_s$?

Question 4

Consider the Itô integral $\int_0^T H_s dM_s$, where $M_s$ is a square-integrable martingale. What is the expected value of this integral, assuming $H_s$ is a suitable integrand?

Question 5

The construction of the Itô integral often begins by defining it for a specific class of integrands. Which of the following classes is typically used as the starting point for this construction?