Question

A stock price S is governed where z is a standardized Wiener process. Find the process that governs G(t)

Answer 1

This question is incomplete, the complete question is;

A stock price S is governed by dS = aSdt + bSdz

where z is a standardized Wiener process. Find the process that governs G(t) = S^1/2(t)

Answer:

G = S^1/2

Step-by-step explanation:

Solving the Equation

dS = aSdt + bSdz

First we Take S common from Right hand Side

dS = S(a dt + b dz)

Then we also take S Left Hand Side(LHS) from RHS

dS/S = a dt + b dz

So d = a dt + b dz

now we Take d Common from RHS

d = d(a t + b z)

So

d/d = a t + b z

1 = a t + b z

So, t = (1-b z) / a

Now  substitute value of t in equation G(t) = S^1/2(t)

we have

G{(1- b z)/a} = S^1/2 {(1- b z)/a}

(1- b z)/a) from both sides cancels out each other

So we have  G = S^1/2