in the attached file, when it says that "if we choose p so that" what does it mean? and after this statement how he calculated S_o ?

@KingGeorge @TuringTest can you please help me?

By choosing a certain value for p, you can sometimes force a certain outcome. So the writers of the book chose p to force the equation on the next line to be true.

sorry I didn't get it...@KingGeorge

We can't really give you more info other than what kingeorge did since we can't see the whole page. For example there are differential equations like the schrodinger equation that require us to plug in certain values in order to solve it.

I guess the same thing applies here.

Suppose I have an equation \(y=x+5\). Then I can choose an \(x\) so that \(y=8\). In this case, I can choose \(x=3\), but the statement "I choose an \(x\) so that" says that we don't care what the value of \(x\) is. We just know that there exists some \(x\) that makes the statement true.

Perhaps it would be more helpful to you if you thought of it as "There exists some p where the following equality holds" (where p has to be in the domain of possible numbers to choose from)

@Romero now?

thanks @KingGeorge

You're welcome. Does it make more sense now?

yes, it does but I still don't understand that where has the unhighligted part in equation 1.1.5 has gone?

Since \[S_0=\frac{1}{1+r}(\hat p S_1(H)+\hat qS_1(T))\]The highlighted part becomes\[\frac{1}{1+r}(\hat p S_1(H)+\hat qS_1(T))- S_0\]\[=\frac{1}{1+r}(\hat p S_1(H)+\hat qS_1(T))-\frac{1}{1+r}(\hat p S_1(H)+\hat qS_1(T))=0\]By substituting in that formula for \(S_0\)

This turn 1.1.5 into\[X_0+\Delta_0\cdot0=X_0=\frac{1}{1+r}[\hat p V_1(H)+\hat qV_1(T)]\]

got it...God bless u

Join our real-time social learning platform and learn together with your friends!