New bounds for the probability that at least image-out-of-image events occur with unimodal distributions

The contribution of the shape information of the underlying distribution in probability bounding problem is investigated and a linear programming based bounding methodology to obtain robust and efficiently computable bounds for the probability that at least image-out-of-image events occur is developed. The dual feasible basis structures of the relaxed versions of linear programs involved are fully described. The bounds for the probability that at least image-out-of-image events occur are obtained in the form of formulas and as the customized algorithmic solutions of the LP's formulated. An application in finance is presented.