A parallel non-convex approximation framework for risk parity portfolio design

In this paper, we propose a parallel non-convex approximation framework (NCAQ) for optimization problems whose objective is to minimize a convex function plus the sum of non-convex functions. Based on the structure of the objective function, our framework transforms the non-convex constraints to the logarithmic barrier function and approximates the non-convex problem by a parallel quadratic approximation scheme, which will allow the original problem to be solved by accelerated inexact gradient descent in the parallel environment. Moreover, we give a detailed convergence analysis for the proposed framework. The numerical experiments show that our framework outperforms the state-of-art approaches in terms of accuracy and computation time on the high dimension non-convex Rosenbrock test functions and the risk parity problems. In particular, we implement the proposed framework on CUDA, showing a more than 25 times speed-up ratio and removing the computational bottleneck for non-convex risk-parity portfolio design. Finally, we construct the high dimension risk parity portfolio which can consistently outperform the equal weight portfolio in the application of Chinese stock markets.