A note on the connectedness of chance constraints

Abstract

We prove a result on connectedness of (functional) chance constraints $ P(h(x) \ge g(\xi) \ge p$, where the decision variable $x$ belongs to a Banach space and $h$ is assumed to be strictly quasiconcave. The derived characterization completely relies on a constraint qualification for the mapping $h$. There are no assumptions on the distribution of $\xi$ involved. For the purpose of illustration, a generic application is briefly discussed. Limiting counter-examples are provided and a simple criterion for the constraint qualification to hold is given in case of linear $h$.