Joint stochastic orders of high degrees and their applications in portfolio selections

In this paper, we propose two new classes of joint stochastic orders, namely joint (reversed) hazard order of degree n and joint n-increasing convex/concave order, and establish their theoretical properties. These new orders substantially generalize the existing class of joint stochastic orders, and incorporate them in one general framework. We also explore the applications of these orders in portfolio selections and unify similar studies on this problem.