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

## TL;DR

This paper develops a convex duality framework for pricing contingent claims when the seller has partial information and faces short selling restrictions, providing a dual characterization of the price.

## Contribution

It introduces a duality approach using conjugate duality theory to handle partial information and short selling constraints in pricing problems.

## Key findings

- Derived a dual problem for the constrained stochastic optimization
- Established conditions for strong duality to hold
- Provided a martingale-based characterization of the claim price

## 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.