Broker-Trader Partial Information Nash-Equilibria

Xuchen Wu and Sebastian Jaimungal

Papers from arXiv.org

Abstract: We study partial information Nash equilibrium between a broker and an informed trader. In this setting, the informed trader, who possesses knowledge of a trading signal, trades multiple assets with the broker in a dealer market. Simultaneously, the broker offloads these assets in a lit exchange where their actions impact the asset prices. The broker, however, only observes aggregate prices and cannot distinguish between underlying trends and volatility. Both the broker and the informed trader aim to maximize their penalized expected wealth. Using convex analysis, we characterize the Nash equilibrium and demonstrate its existence and uniqueness. Furthermore, we establish that this equilibrium corresponds to the solution of a nonstandard system of forward-backward stochastic differential equations (FBSDEs) that involves the two differing filtrations. For short enough time horizons, we prove that a unique solution of this system exists. Finally, under quite general assumptions, we show that the solution to the FBSDE system admits a polynomial approximation in the strength of the transient impact to arbitrary order, and prove that the error is controlled.

Date: 2024-12, Revised 2025-04
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2412.17712 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:2412.17712

Access Statistics for this paper

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