The insider problem in the trinomial model: a discrete-time jump process approach

H\'el\`ene Halconruy

Papers from arXiv.org

Abstract: In an incomplete market underpinned by the trinomial model, we consider two investors : an ordinary agent whose decisions are driven by public information and an insider who possesses from the beginning a surplus of information encoded through a random variable for which he or she knows the outcome. Through the definition of an auxiliary model based on a marked binomial process, we handle the trinomial model as a volatility one, and use the stochastic analysis and Malliavin calculus toolboxes available in that context. In particular, we connect the information drift, the drift to eliminate in order to preserve the martingale property within an initial enlargement of filtration in terms of the Malliavin derivative. We solve explicitly the agent and the insider expected logarithmic utility maximisation problems and provide a hedging formula for replicable claims. We identify the insider expected additional utility with the Shannon entropy of the extra information, and examine then the existence of arbitrage opportunities for the insider.

Date: 2021-06, Revised 2023-09
New Economics Papers: this item is included in nep-cwa and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Decisions in Economics and Finance, 46, 379-413, 2023

Downloads: (external link)
http://arxiv.org/pdf/2106.15208 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:2106.15208

Access Statistics for this paper

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