  We consider a diffusion approximation to an insurance risk model where an
external driver models a stochastic environment. The insurer can buy
reinsurance. Moreover, investment in a financial market is possible. The
financial market is also driven by the environmental process. Our goal is to
maximise terminal expected utility. In particular, we consider the case of
SAHARA utility functions. In the case of proportional and excess-of-loss
reinsurance, we obtain explicit results.
