Optimal Portfolios in Lévy Markets under State-Dependent Bounded Utility Functions

José E. Figueroa-López and Jin Ma

International Journal of Stochastic Analysis, 2010, vol. 2010, 1-27

Abstract:

Motivated by the so-called shortfall risk minimization problem, we consider Merton's portfolio optimization problem in a non-Markovian market driven by a Lévy process, with a bounded state-dependent utility function. Following the usual dual variational approach , we show that the domain of the dual problem enjoys an explicit “parametrization,†built on a multiplicative optional decomposition for nonnegative supermartingales due to Föllmer and Kramkov (1997). As a key step we prove a closure property for integrals with respect to a fixed Poisson random measure, extending a result by Mémin (1980). In the case where either the Lévy measure ν of Z has finite number of atoms or Δ S t / S t − = ζ t ϑ ( Δ Z t ) for a process ζ and a deterministic function ϑ , we characterize explicitly the admissible trading strategies and show that the dual solution is a risk-neutral local martingale.

Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/2010/236587.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/2010/236587.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:236587

DOI: 10.1155/2010/236587

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().