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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60H05 Stochastic integrals
- 90A09 Finance, portfolios, investment

**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