I am currently trying to adapt a model to a long short portfolio strategy. The model is stated here: A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem by Jiang, Xu, and Liang https://arxiv.org/abs/1706.10059
In Eq. (1-10), the portfolio process is formulated. The portfolio weight vector w can have only positive values in this long-only setting. Instead, I now adapted the network to output a weight vector of positive and negative values whose absolute values sum up to one, where positive (negative) values represent going long (short). When looking at the equations, one quickly sees that the portfolio equations do not work correctly anymore if the weight vector can have negative values, mostly because of the definition of yt, which is the price return expressed as a factor from time t-1 to t. For instance, yt = vt/v[t-1] where v are the prices of the individual assets. As a first fix, I tried to take 1/yt instead of yt whenever the corresponding weight is negative. Then, in the following equations, I can simply use the absolute of the vector w, and the equations should come out right then. However, in this way, i believe, the network does not really learn to set the weights correctly. Instead, now, i am trying to reformulate the equations correctly for a weight vector that can take negative values, as well. My first try was to replace yt*wt by 1 + (yt-1) * wt in all the equations. This seems to work (although I am not sure whether the values of the short positions are then correctly computed), but for Eq.(7), it fails. So there must be a different, more elegant approach to adapt the model to long short without having to change much in the loss functions, portfolio value computation, etc. Any ideas? I appreciate it!