  We develop a methodology for detecting asset bubbles using a neural network.
We rely on the theory of local martingales in continuous-time and use a deep
network to estimate the diffusion coefficient of the price process more
accurately than the current estimator, obtaining an improved detection of
bubbles. We show the outperformance of our algorithm over the existing
statistical method in a laboratory created with simulated data. We then apply
the network classification to real data and build a zero net exposure trading
strategy that exploits the risky arbitrage emanating from the presence of
bubbles in the US equity market from 2006 to 2008. The profitability of the
strategy provides an estimation of the economical magnitude of bubbles as well
as support for the theoretical assumptions relied on.
