A Tchebysheff-type bound on the expectation of sublinear polyhedral functions

This work presents an upper bound on the expectation of sublinear polyhedral functions of multivariate random variables based on an inner linearization and domination by a quadratic function. The problem is formulated as a semi-infinite program which requires information on the first and second moments of the distribution, but without the need of an independence assumption. Existence of a solution and stability of this semi-infinite program are discussed. The authors show that an equivalent optimization problem with a nonlinear objective function and a set of linear constraints may be used to generate solutions.