The standard mean-variance approach can imply extreme weights in some assets in the optimal allocation and a lack of stability of this allocation over time. In order to not only improve the robustness of the portfolio allocation, but also to better control the portfolio turnover and the sensitivity of the portfolio to systematic risk, it is proposed in this chapter to introduce additional constraints on both the total systematic risk contribution of the portfolio and its turnover. Our chapter extends the existing literature on risk parity in three directions: (1) we consider other risk criteria than the variance, such as the value-at-risk (VaR), or the expected shortfall; (2) we manage separately the systematic and idiosyncratic components of the portfolio risk; (3) we introduce a set of portfolio management approaches which control the degree of market neutrality of the portfolio, for the strength of the constraint on systematic risk contribution and for the turnover