Kristina R. Dahl: Duality methods for pricing contingent claims under short selling constraints


Abstract: We begin with an introduction to conjugate duality theory, which is a topic in convex analysis that can be used for a wide range of applications. Then, this theory is used to analyse the pricing problem of a seller with a general level of inside information, who is not allowed to sell short in certain assets. The problem is considered for arbitrary scenario space in discrete time. 
A dual problem to the pricing problem is derived using conjugate duality, and we prove that there is no duality gap. This gives a characterization of the insider's price of a contingent claim under short selling constraints, involving martingale- and super martingale conditions on the price process. We compare the prices offered by a constrained and an unconstrained seller. We also compare the prices offered by two sellers with different information levels. It turns out that these results can provide understanding of the origin of price bubbles in a financial market.