The first moment and second central moments of the portfolio return, a.k.a. mean variance, have been widely employed to assess expected profit risk portfolio. Investors pursue higher lower variance when designing portfolios. two can well describe distribution return it follows Gaussian distribution. However, real world assets is usually asymmetric heavy-tailed, which far from being a asymmetry ...

The rank function rank(·) is neither continuous nor convex which brings much difficulty to the solution of rank minimization problems. In this paper, we provide a unified framework to construct the approximation functions of rank(·), and study their favorable properties. Particularly, with two families of approximation functions, we propose a convex relaxation method for the rank minimization p...

We describe two nonconventional algorithms for linear regression, called GAME and CLASH. The salient characteristics of these approaches is that they exploit the convex `1-ball and non-convex `0-sparsity constraints jointly in sparse recovery. To establish the theoretical approximation guarantees of GAME and CLASH, we cover an interesting range of topics from game theory, convex and combinatori...