On spline approximation for bivariate functions of increasing convex type

Abstract

The motivation of the paper is to construct the largest and smallest families of functions that allow us to generate the bivariate continuous stochastic orderings of increasing convex type introduced recently in Denuit et al. (1999). The main step will consist in deriving a spline approximation for bivariate continuous increasing convex functions, which extends to the bivariate case a fundamental result obtained by Popoviciu (1941).

Keywords

• stochastic orderings
• extremal generators
• convexity
• bivariate continuous increasing convex functions
• spline approximation