We study a quadratic BSDE in a continuous filtration with an unbounded generatorand an infinite time horizon. This equation comes from a stochasticcontrol problem in the context of robust utility maximisation.[...]

We study the exponential utility indifference valuation of a contingentclaim H when asset prices are given by a general semimartingale S. Under mildassumptions on H and S, we prove that a no-arbitrage type condition is fulfilled ifand only if H has a certain representation. In this case, the...