Log-optimal and numéraire portfolios for market models stopped at a random time

Tahir Choulli () and Sina Yansori
Additional contact information
Tahir Choulli: University of Alberta
Sina Yansori: University of Alberta

Finance and Stochastics, 2022, vol. 26, issue 3, No 5, 535-585

Abstract: Abstract This paper focuses on numéraire and log-optimal portfolios when a market model ( S , F , P ) $(S,\mathbb{F},P)$ – specified by its assets’ price S $S$ , its flow of information F $\mathbb{F}$ and a probability measure P $P$ – is stopped at a random time τ $\tau $ . The flow of information that incorporates both F $\mathbb{F}$ and τ $\tau $ , denoted by G $\mathbb{G}$ , is the progressive enlargement of F $\mathbb{F}$ with τ $\tau $ . For the resulting stopped model ( S τ , G , P ) $(S^{\tau},\mathbb{G},P)$ , we study the two portfolios in different manners and describe their computations in terms of F $\mathbb{F}$ -observable parameters of the pair ( S , τ ) $(S, \tau )$ . In particular, we single out the types of risks induced by τ $\tau $ that really affect the numéraire portfolio, and address the following questions: 1) What are the conditions on τ $\tau $ (preferably in terms of information-theoretic concepts such as entropy) that guarantee the existence of the log-optimal portfolio for ( S τ , G , P ) $(S^{\tau},\mathbb{G},P)$ when that for ( S , F , P ) $(S,\mathbb{F},P)$ already exists? 2) What are the factors that fully determine the increment in maximal expected logarithmic utility from terminal wealth for the models ( S τ , G , P ) $(S^{\tau},\mathbb{G},P)$ and ( S , F , P ) $(S,\mathbb{F},P)$ , and how can one quantify them?

Keywords: Random horizon; Log-optimal portfolio; Numéraire portfolio; Deflators; Informational risks; Utility; Progressive enlargement of filtration; Asymmetric information; Semimartingales and predictable characteristics; 60G48; 60H05; 91B16; 91G10; 91G40; 94A17 (search for similar items in EconPapers)
JEL-codes: D82 D89 G11 G14 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-022-00477-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:finsto:v:26:y:2022:i:3:d:10.1007_s00780-022-00477-8

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-022-00477-8

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().