1) The evolution of the risk-free asset is modeled by the process {Bt}t0 defined by Bt=exp(0trsds) where {rt}t0 represents the process of the instantaneous interest rate of the risk-free asset. This process satisfies the ordinary differential equation, drt=k(rt)dt. A) Show that the solution rt=+(r0)ekt, satisfies the ordinary differential equation drt=k(rt)dt. B) Show that the evolution of the price of the risk-free asset {Bt}t0 satisfies the ordinary differential equation, dBt=rtBtdt. C) The evolution of the price of the risky asset {St}t0 satisfies the stochastic differential equation, dSt=Stdt+StdWtP, where {WtP}t0 is a Brownian motion on the probability space (,F,P). Determine the stochastic differential equation followed by the process {St}t0, where St=St/Bt. D) Use Girsanov's theorem to show how it is possible to change the probability measure on (,F) in order to obtain the evolution of the price of the risky asset under the risk measure neutral Q. In addition, give the stochastic differential equation satisfied by the evolution of the price of the risky asset {St}t0 under the neutral risk measure Q. Clearly justify your approach