A generalisation of the chance-constrained Charnes-Cooper approach

TL;DR

This paper extends the Charnes-Cooper chance-constrained method to elliptically contoured distributions, creating a more flexible and distribution-invariant approach for stochastic linear programming.

Contribution

It introduces a generalized, distribution-invariant relaxation of stochastic linear programming applicable to elliptically contoured distributions.

Findings

The approach is invariant under the entire class of elliptically contoured distributions.

It broadens the applicability of chance-constrained methods in stochastic programming.

The method maintains tractability and robustness across different distributional assumptions.

Abstract

A generalisation of the Charnes-Cooper chance-constrained approach is proposed in the setting of the family of elliptically contoured distributions. The new relaxed stochastic linear programming is notably invariant under the entire class of probability distributions.