a) Consider for ER, a>0 the partial differential equation ad 1 + 2 + of at ,22 -0. 8.2 f(T.x)= In(a) Find for t 0, z>0 the solution f(t,r) by applying the Feynman-Kac theorem. b) Assume a Black-Scholes model with ER, r>0, So > 0, a>0 and consider a European- style financial derivative with payoff p(Sr). Determine all possible choices a ER such that So is the price of the derivative at time t < T.