# Log-optimal portfolio and num\'eraire portfolio under random horizon

Tahir Choulli and Sina Yansori

Papers from arXiv.org

Abstract: This paper considers an initial market model, specified by the pair $(S,\mathbb F)$ where $S$ is its discounted assets' price process and $\mathbb F$ its flow of information, and an arbitrary random time $\tau$. This random time can represent the death time of an agent or the default time of a firm, and in both cases $\tau$ can not be seen before it occurs. Thus, the progressive enlargement of $\mathbb F$ with $\tau$, denoted by $\mathbb G$, sounds tailor-fit for modelling the new flow of information that incorporates both $\mathbb F$ and $\tau$. For the stopped model $(S^{\tau},\mathbb G)$, we describe in different manners and as explicit as possible the num\'eraire portfolio, the log-optimal portfolio, the log-optimal deflator (which is the dual of the log-optimal portfolio), and we elaborate their duality without any further assumption.

Date: 2018-10
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
http://arxiv.org/pdf/1810.12762 Latest version (application/pdf)

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:arx:papers:1810.12762

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().

Page updated 2018-11-24
Handle: RePEc:arx:papers:1810.12762