A convex duality approach for pricing contingent claims under partial information and short selling constraints

ABSTRACT

We consider the pricing problem facing a seller of a contingent claim. We assume that this seller has some general level of partial information, and that he is not allowed to sell short in certain assets. This pricing problem, which is our primal problem, is a constrained stochastic optimization problem. We derive a dual to this problem by using the conjugate duality theory introduced by Rockafellar. Furthermore, we give conditions for strong duality to hold. This gives a characterization of the price of the claim involving martingale- and super-martingale conditions on the optional projection of the price processes.

KEYWORDS:

• Convex duality
• mathematical finance
• pricing
• partial information

Mathematics Subject Classification:

• 49N15
• 90C15
• 90C25
• 90C46
• 91G20

Funding

The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 228087.