Before revision:  For this purpose, we combine three different deep neural network structures in a novel way: a feedforward network to capture non-linearities, a recurrent Long-Short-Term-Memory network to find a small set of  economic state processes and a generative adversarial network to identify the portfolio strategies with the least explained pricing information .
After revision:  Our asset pricing model outperforms out-of-sample all other benchmark approaches in terms of Sharpe ratio, explained variation and pricing errors. We trace its superior performance to including the no-arbitrage constraint in the estimation and to accounting for macroeconomic conditions and non-linear interactions between firm-specific characteristics. Our generative adversarial network enforces no-arbitrage by identifying the portfolio strategies with the most pricing information. Our recurrent Long-Short-Term-Memory network to find a small set of economic state processes and a generative adversarial network to identify the portfolio strategies with the least explained pricing information .