Consider a portfolio II consisting of an option V and A amount of stock S, i.e. II4 = VE + Ax St. The stock pays no dividend and its price follows the lognormal stochastic differential equation dSt = Sidt + o SidW. (a) Use Its formula to write down the SDE for the process dVi. (b) Write down the process dllt, and determine what choice of A will give rise to a risk-free portfolio. (c) A risk-free portfolio must earn the continuously compounded risk-free rate by no-arbitrage. Show that this leads to the Black-Scholes partial differential equation. Consider a portfolio II consisting of an option V and A amount of stock S, i.e. II4 = VE + Ax St. The stock pays no dividend and its price follows the lognormal stochastic differential equation dSt = Sidt + o SidW. (a) Use Its formula to write down the SDE for the process dVi. (b) Write down the process dllt, and determine what choice of A will give rise to a risk-free portfolio. (c) A risk-free portfolio must earn the continuously compounded risk-free rate by no-arbitrage. Show that this leads to the Black-Scholes partial differential equation