  We consider a Poisson process $\eta$ on a measurable space
$(\BY,\mathcal{Y})$ equipped with a partial ordering, assumed to be strict
almost everwhwere with respect to the intensity measure $\lambda$ of $\eta$. We
give a Clark-Ocone type formula providing an explicit representation of square
integrable martingales (defined with respect to the natural filtration
associated with $\eta$), which was previously known only in the special case,
when $\lambda$ is the product of Lebesgue measure on $\R_+$ and a
$\sigma$-finite measure on another space $\BX$. Our proof is new and based on
only a few basic properties of Poisson processes and stochastic integrals. We
also consider the more general case of an independent random measure in the
sense of It\^o of pure jump type and show that the Clark-Ocone type
representation leads to an explicit version of the Kunita-Watanabe
decomposition of square integrable martingales. We also find the explicit
minimal variance hedge in a quite general financial market driven by an
independent random measure.
