In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in Chen et al. (2008) . Three issues are investigated. The first issue is the (non-)uniqueness of the optimal solution. The second issue is the generalization to an optimization problem where the weights may be random. This theory is then applied to static super-replication strategies for some

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... options in a stochastic interest rate setting. The third issue is the study of the co-existence of the comonotonicity property and the martingale property.