Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Hedging and Optimal Investment in Infinite Assets Model with Jumps


Code(s) de Classification MSC:

Résumé: Motivated by the theory of bond markets, we consider an infinite assets model driven by marked point process and Wiener process. The self-financed wealth processes are defined by using measure-valued strategies. Going further on the works of Bjork et al. [1]-[2] who focus on the existence of martingale measures and market completeness questions, we study here the incompleteness case. More precisely, we state a decomposition theorem for supermartingales in our infinite assets model context. The concept of approximate wealth processes is introduced. As in the case of stock markets, one can then derive a dual representation of the super-replication cost and study the problem of utility maximization by duality methods.

Mots Clés: Bond markets ; measure-valued portfolio ; jump-diffusion model ; stochastic integral ; incomplete market ; optional decomposition ; utility maximization

Date: 2002-10-01

Prépublication numéro: PMA-757

Pdf file : PMA-757.pdf