Economics Insights @ CBS

We determine the minimum cost of super-replicating a nonnegative contingent claim when there are convex constraints on portfolio weights. We show that the optimal cost with constraints is equal to the price of a related claim without constraints. The related claim is a dominating claim, that is, a claim whose payoffs are increased in an appropriate way relative to the original claim. The results hold for a variety of options, including some path-dependent options.

We consider a distribution system consisting of a single warehouse and many geographically dispersed retailers. Each retailer faces demands for a single item which arise a deterministic, retailer specific rate. The retailers' stock is replenished by a fleet of vehicles of limited capacity, departing and returning to the warehouse and combining deliveries into efficient routes. The cost of any given route consists of a fixed component and a component which is proportional with the total distance driven. Inventory costs are proportional with the stock levels.

Past research has found that when people imagine how an outcome might have turned out differently, their "if only" thoughts consistently focus on particular types of antecedent conditions. The authors propose that one principle people follow is to focus on an antecedent that fails to correspond in magnitude to the imagined counterfactual outcome. Specifically, they propose that people focus on such antecedents and change them in the direction of increasing correspondence to the imagined counterfactual outcome.