5
$\begingroup$

In his paper, Eugene Fama gives the definition of a "fair game" as given below. I disagree. AFAIK, a martingale has the following property: $E[X_{t+\tau} | X_t] = X_t$. What am I missing?

enter image description here

Footnote 9 says:

enter image description here enter image description here

And again, in a previous statement:

enter image description here

$\endgroup$
3
  • 1
    $\begingroup$ What does Footnote 9 say? $\endgroup$
    – nbbo2
    Jul 15, 2020 at 17:47
  • $\begingroup$ @noob2 Nothing that would justify the zero in my opinion. I've updated. $\endgroup$
    – s5s
    Jul 15, 2020 at 18:00
  • $\begingroup$ What does it mean for martingales to be "incorrect"? $\endgroup$ Jul 16, 2020 at 5:46

1 Answer 1

6
$\begingroup$

The way I understand it is:

In equation 2 $x_{j, t + 1}$ is defined as the change in of $p_j$ over the period $t$ to $t + 1$. The formula says that the expectation of the change is zero which is the same as saying that the expectation of the original variable at $t+1$ is equal to its current value.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.