2. Stochastic Processes

Martingale Theory — Quiz

Test your understanding of martingale theory with 5 practice questions.

Practice Questions

Question 1

Which theorem in mathematical finance states that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure?

Question 2

What does the Doob decomposition theorem assert for a discrete-time integrable submartingale $\\{X_n\\}$?

Question 3

Which of the following correctly characterizes a martingale process?

Question 4

Let $\\{M_n\\}$ be a martingale and $\\{H_n\\}$ a process. Under what condition on $H_n$ is the discrete stochastic integral $X_n=\sum_{k=1}^n H_{k-1}(M_k-M_{k-1})$ also a martingale?

Question 5

If $\\{M_n\\}$ is a martingale and $\varphi$ is a convex function, which process is a submartingale?