Duplicating and pricing contingent claims with constrained portfolios

The problem of pricing contingent claims is studied in the situation where the constrains imposed on an investor's portfolios cannot be neglected. The following results are obtained: ( i ) under elastic rules, the cost to dup licate a contingent claim exists and is unique; ( ii ) this cost depends no nlinearly and convexly on the contingent claim; ( iii ) the cost under rigi d rules is the limit of the corresponding elastic rules when passing the pe nalty to infinity. This cost is also a nonlinear and convex functional of t he contingent claim. Due to nonlinearity, the cost of duplication may or ma y not be the non-arbitrage price of the contingent claim. it depends on how the market organizes the production of contingent claims. The conclusion t hat the cost of duplication is a convex functional of the contingent claim provides an explanation why securitiezed financial services are often high profitable business.