I'm getting very confused with the inconsistent notation being used throughout the solutions of past year exam question solutions. In particular, I want to know when we condition the share price\([S_t]\) distribution at time \(t>u\) on \(S_u\), and when we don't. I'm not sure if I've explicitly expressed my doubt here. However, any input from you would be delightful. Thanka you for reading.
Yes. Currently I am looking at Question 3 part (i), September 2011. The question asks for distribution of \(S_t\), however, isn't it supposed to be \(S_t|S_0\)? Pretty confused
Oh, I see what you mean. \(S_t\) is a random process, but it has to start somewhere, and so will always depend to some extent on its initial value \(S_0\). In the question you mention, the expression for \(S_t\) depends on \(S_0\), but the distribution doesn't appear to because \(S_0=1\). The conditioning is implied. Does that help?
But isn't this mathematically incorrect to not denote that \(S_t|S_0\) ? I understand what you're saying though, that we don't need to explicitly mention this particular conditioning all the time? Is that correct? Thanks for the help.
It is certainly more precise to include the conditioning, and the fact that it isn't always done is unfortunate.
