Suppose a stock price follows the Ito process dS = aS dt + bS dB, (1) where a, b, , are all constants non-zero

Suppose a stock price follows the Itˆo process dS = aSα dt + bSβ dB, (1) where a, b, α, β are all constants non-zero constants, and α, β 6= 0, 1. Find F(S), a differentiable function of the stock price, such that dF is an Itˆo process with constant volatility σ. What PDE would be satisfied by the price of options on the sto