  We prove results on bounded solutions to backward stochastic equations driven
by random measures. Those bounded BSDE solutions are then applied to solve
different stochastic optimization problems with exponential utility in models
where the underlying filtration is noncontinuous. This includes results on
portfolio optimization under an additional liability and on dynamic utility
indifference valuation and partial hedging in incomplete financial markets
which are exposed to risk from unpredictable events. In particular, we
characterize the limiting behavior of the utility indifference hedging strategy
and of the indifference value process for vanishing risk aversion.
