  In this paper we study a risk-minimizing hedging problem for a semimartingale
incomplete financial market where d+1 assets are traded continuously and whose
price is expressed in units of the num\'{e}raire portfolio. According to the
so-called benchmark approach, we investigate the (benchmarked) risk-minimizing
strategy in the case where there are restrictions on the available information.
More precisely, we characterize the optimal strategy as the integrand appearing
in the Galtchouk-Kunita-Watanabe decomposition of the benchmarked claim under
partial information and provide its description in terms of the integrands in
the classical Galtchouk-Kunita-Watanabe decomposition under full information
via dual predictable projections. Finally, we apply the results in the case of
a Markovian jump-diffusion driven market model where the assets prices dynamics
depend on a stochastic factor which is not observable by investors.
