A note on super-hedging for investor-producers

TL;DR

This paper extends super-hedging theory to include production systems in continuous markets, enabling more accurate pricing and hedging of derivatives on produced goods like electricity.

Contribution

It introduces the concept of conditional sure profit and generalizes super-hedging results to markets with production, providing dual characterizations and applications to power futures.

Findings

Established a closedness property for super-hedgeable claims.

Provided a dual characterization of super-hedgeable claims.

Applied results to power futures pricing.

Abstract

We study the situation of an agent who can trade on a financial market and can also transform some assets into others by means of a production system, in order to price and hedge derivatives on produced goods. This framework is motivated by the case of an electricity producer who wants to hedge a position on the electricity spot price and can trade commodities which are inputs for his system. This extends the essential results of Bouchard & Nguyen Huu (2011) to continuous time markets. We introduce the generic concept of conditional sure profit along the idea of the no sure profit condition of R\`asonyi (2009). The condition allows one to provide a closedness property for the set of super-hedgeable claims in a very general financial setting. Using standard separation arguments, we then deduce a dual characterization of the latter and provide an application to power futures pricing.