On an optimization problem related to static super-replicating strategies

• We investigate three issues related to super-replicating strategies for options written on a weighted sum of asset prices.
• 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.
• The third issue is the study of the co-existence of the comonotonicity property and the martingale property.

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 exotic 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.