A study of robust portfolio optimization with European options using polyhedral uncertainty sets

•We combine two techniques to address risk in portfolio management: robust optimization and European options.•We study three models: a strong guarantee model, a weak guarantee model and a combined strong and weak guarantee model.•We provide theoretical insights into diversification, focusing on the number of calls and puts for each asset at optimality.•We show our models perform very well compared to benchmarks including those in Zymler et al. [24] in a case study. in a case study.