  This paper is concerned with the study of insurance related derivatives on
financial markets that are based on non-tradable underlyings, but are
correlated with tradable assets. We calculate exponential utility-based
indifference prices, and corresponding derivative hedges. We use the fact that
they can be represented in terms of solutions of forward-backward stochastic
differential equations (FBSDE) with quadratic growth generators. We derive the
Markov property of such FBSDE and generalize results on the differentiability
relative to the initial value of their forward components. In this case the
optimal hedge can be represented by the price gradient multiplied with the
correlation coefficient. This way we obtain a generalization of the classical
'delta hedge' in complete markets.
