In the paper, "On the properties of equally-weighted risk contributions portfolios, authors Maillard, Roncalli and Teiletche give a numerical solution for computing the weights of an ERC-based portfolio. I've two questions that I need some assistance with- 1) How do I introduce leverage in their numerical solution? If I just relax the contraints of having positive weights, will that cause any loss of generality of the numerical solution? I don't think so, but I want to check. I also wonder why the authors don't consider leverage in this paper or any of their following papers.2) How do I introduce the concept of having a target portfolio volatility in the numerical solution? I've been thinking of using the amplifying the ex-ante weights to get the target vol, but won't that end up violating the constraint that sum of weights = 1. Again, I could not find any research that explains how this can be achieved using Maillard, Roncalli et al's numerical solution.Please let me know if you have any thoughts or ideas. thanks,