Confusion regarding notation

[Adienl]

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.

 

[Steve Hales]

It depends on what you want to do with it. Have you got any examples?

 

[Adienl]

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

 

[Adienl]

It depends on what you want to do with it. Have you got any examples?

Also, thanks for replying so fast.

 

[Steve Hales]

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?

 

[Adienl]

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.

 

[Steve Hales]

It is certainly more precise to include the conditioning, and the fact that it isn't always done is unfortunate.

 

[Adienl]

It is certainly more precise to include the conditioning, and the fact that it isn't always done is unfortunate.

Thank you sir