Optimal Portfolios in Lévy Markets under State-Dependent Bounded Utility Functions
Joint Authors
Ma, Jin
Figueroa-López, José E.
Source
International Journal of Stochastic Analysis
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-27, 27 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-03-15
Country of Publication
Egypt
No. of Pages
27
Main Subjects
Abstract EN
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 ΔSt/St−=ζtϑ(ΔZt) 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.
American Psychological Association (APA)
Figueroa-López, José E.& Ma, Jin. 2010. Optimal Portfolios in Lévy Markets under State-Dependent Bounded Utility Functions. International Journal of Stochastic Analysis،Vol. 2010, no. 2010, pp.1-27.
https://search.emarefa.net/detail/BIM-456176
Modern Language Association (MLA)
Figueroa-López, José E.& Ma, Jin. Optimal Portfolios in Lévy Markets under State-Dependent Bounded Utility Functions. International Journal of Stochastic Analysis No. 2010 (2010), pp.1-27.
https://search.emarefa.net/detail/BIM-456176
American Medical Association (AMA)
Figueroa-López, José E.& Ma, Jin. Optimal Portfolios in Lévy Markets under State-Dependent Bounded Utility Functions. International Journal of Stochastic Analysis. 2010. Vol. 2010, no. 2010, pp.1-27.
https://search.emarefa.net/detail/BIM-456176
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-456176