0
$\begingroup$

In my course on discrete-time finance we derived the following equality for a lower bound for the value of a not necessarily replicable contingent claim $D$. Here we are looking at a single period market with risk-free interest rate $r$ and $E$ is the expectation operator. $$\sup\{E[Y(1)/(1+r)]:Y \text{ replicable, }\text Y\le D\} \\ = \inf\{E_{Q'}[D(1)/(1+r))]:Q' \text{ risk free P-measure}\text \}$$ My question: Which probability measure do we use to compute the first expectation on the left? Is it a risk-neutral one, or is it the real one?

$\endgroup$
0
$\begingroup$

Coming back to this question way later, I managed to resolve my confusion. Using a well-known theorem we have that $E_{Q}[Y(1)]$ is constant on $\mathbb{M}$. Thus, it is irrelevant which measure we are using, since the resulting bound will be the same.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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