The answer in the case of the call is yes and in the case of the general martingale quotient f/g (with g being the numeraire asset) is yes also provided s/g is a martingale also and we can represent the quotient f/g as a stochastic integralf(t)/g(t) = integral_0^t phi(u)d(s(u)/g(u)) (*)phi(t) is then the number of shares held in the underlying s while psi(t) = f(t)/g(t) - phi(t)(s(t)/g(t))is the number of shares held in the numeraire asset g.It is easy to check that the strategy is selffinancing (check it in the discounted market (s/g,g/g)=(s/g,1)).The possibility of the integral representation (*) often follows from general martingale representation theorems.

in general no. If we are working in a sufficiently simple continuous world as in your example then yes.Simple example:stock 100 today. 110,100, or 90 tomorrow with equal probability. g = riskless bond always worth 1f = call option struck at 100 we can make f a martingale by making it worth 10/3 today but any price between 0 and 5 is not arbitrageable so we cannot eliminate risk by hedging.MJ