Mathematics – Probability
Scientific paper
2008-06-16
Annals of Applied Probability 2008, Vol. 18, No. 3, 929-966
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/07-AAP469 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/07-AAP469
We consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth, with utility functions that are finite-valued over $(a,\infty)$, $a\in\lbrack-\infty,\infty)$, and satisfy weak regularity assumptions. We adopt a class of trading strategies that allows for stochastic integrals that are not necessarily bounded from below. The embedding of the utility maximization problem in Orlicz spaces permits us to formulate the problem in a unified way for both the cases $a\in\mathbb{R}$ and $a=-\infty$. By duality methods, we prove the existence of solutions to the primal and dual problems and show that a singular component in the pricing functionals may also occur with utility functions finite on the entire real line.
Biagini Sara
Frittelli Marco
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