  We consider a general class of diffusion-based models and show that, even in
the absence of an Equivalent Local Martingale Measure, the financial market may
still be viable, in the sense that strong forms of arbitrage are excluded and
portfolio optimisation problems can be meaningfully solved. Relying partly on
the recent literature, we provide necessary and sufficient conditions for
market viability in terms of the market price of risk process and martingale
deflators. Regardless of the existence of a martingale measure, we show that
the financial market may still be complete and contingent claims can be valued
under the original (real-world) probability measure, provided we use as
numeraire the Growth-Optimal Portfolio.
