Document ESAIM: P&S, June 2007, Vol. 11, pp. 197-216
DOI: 10.1051/ps:2007015
Entropic Conditions and Hedging
Samuel NjohUniversité de Marne-La-Vallée, Cité Descartes, 5, Bld Descartes, Champs-Sur-Marne, 77454 Marne-La-Vallée Cedex 2, France; njoh@math.univ-mlv.fr
(Received February 16, 2006. Revised September 6 and October 12, 2006. Published online 19 June 2007.)
Abstract
In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential utilities when the risk premium is bounded. Our result is based upon backward stochastic differential equation (BSDE) and a good choice of admissible strategies which allows us to solve our hedging problem.
Mathematics Subject Classification. 90A09, 34A12
Key words: Stochastic optimization, martingale representation theorem.
© EDP Sciences, SMAI 2007