Martingale representation and hedging policies (Q1177217)

A main problem in modern finance mathematics is to give a stochastic integral representation of certain stochastic processes, which are martingales under a Girsanov transform of the original measure. The authors provide a new proof of such an integral representation in the situation where the Girsanov exponential is determined by a Markov integrand. The proof is simple and direct and relies mainly on elementary tools as, e.g., Itô's differentiation rule, rather than on Malliavin's calculus. The obtained formula is used for constructing a hedging portfolio that generates a given contingent claim. The well-known Black- Scholes result is obtained as a particular case.