Consider a security that pays S(T)k at time T (k ≥ 1) where the price S(t) is governed by the standard model dS(t) = μS(

[answerhappygod]

Consider a security that pays S(T)k at time T (k ≥ 1) where the
price
S(t) is governed by the standard model
dS(t) = μS(t)dt + σS(t)dW(t).
Using Black-Scholes-Merton equation, show that the price of this
security at time
t < T is given by
c(t, S(t)) = S(0)ke(k−1)(r+k
2 σ2)(T−t).