arXiv subjects

Bixing Qiao

Publications and source records attributed to Bixing Qiao.

4 recordsLinked to original sources

arXiv2026

Insider and stealth trading with dynamic legal risk

The present paper investigates how insiders strategically navigate ongoing legal risk while leveraging stealth trading within a continuous-time Kyle-type framework. Legal enforcement operates concurrently with trading, which dynamic can be adversely obscured by a large surrounding population of noise traders. While surveillance intensity responds directly to the insider's trading intensity, triggering a random prosecution time, the resulting legal sanctions encompass both strategy-focused criminal penalties and profit-dependent civil penalties. Employing a new impact-neutral measure change, equilibrium analysis shows that even after achieving stealth, the insider internalizes regulatory exposure, and enforcement can significantly shape equilibrium trading strategies. The associated limiting equilibria yield a rich set of outcomes, with three key insights for regulatory impact: (i) under committed regulatory scrutiny, the insider trades a time-varying function of the discrepancy between the asset's fundamental value and its market price, and trading may intensify indefinitely near the end of the trading horizon as legal risk recedes; (ii) merely raising penalties as an advantageous selection cost proves ineffective in offsetting declines in regulatory diligence; (iii) criminal penalties remain essential for deterring aggressive insider trading, as they impose critical temporal constraints on trading intensity not achievable through civil penalties alone.

econ.GN↗

arXiv2025

Heterogeneous Mean Field Games and Local Well-posedness

Motivated by the recent interests in asymmetric mean field games, this paper provides a general framework of Heterogeneous Mean Field Game (HMFG) that subsumes different formulations of graphon mean field games. The key feature of the HMFG is that the players interact with the population through the density ensemble. In this case, the HMFG system becomes an infinite-dimensional Forward-Backward SDE (FBSDE) system. We show that the FBSDE is locally well-posed, thus the HMFG has a unique equilibrium. In addition, we show that the equilibrium of HMFG is a good approximate equilibrium of the corresponding N-Player Game. Lastly, we derive the Itô formula of infinite-dimensional measure flow and use it to obtain the master equation for HMFG as a decoupling field of the infinite-dimensional FBSDE system.

math.OC↗

arXiv2025

A New Approach for the Continuous Time Kyle-Back Strategic Insider Equilibrium Problem

This paper considers a continuous time Kyle-Back model which is a game problem between an insider and a market marker. The existing literature typically focuses on the existence of equilibrium by using the PDE approach, which requires certain Markovian structure and the equilibrium is in the bridge form. We shall provide a new approach which is used widely for stochastic controls and stochastic differential games. We characterize all equilibria through a coupled system of forward backward SDEs, where the forward one is the conditional law of the inside information and the backward one is the insider's optimal value. In particular, when the time duration is small, we show that the FBSDE is wellposed and thus the game has a unique equilibrium. This is the first uniqueness result in the literature, without restricting the equilibria to certain special structure. Moreover, this unique equilibrium may not be Markovian, indicating that the PDE approach cannot work in this case. We next study the set value of the game, which roughly speaking is the set of insider's values over all equilibria and thus is by nature unique. We show that, although the bridge type of equilibria in the literature does not satisfy the required integrability for our equilibria, its truncation serves as a desired approximate equilibrium and its value belongs to our set value. Finally, we characterize our set value through a level set of certain standard HJB equation.

math.OC↗

arXiv2024

Set Values of Dynamic Nonzero Sum Games and Set Valued Hamiltonians

It is well known that the (unique) value of a stochastic control problem or a two person zero sum game under Isaacs condition can be characterized through a PDE driven by the Hamiltonian. Our goal of this paper is to extend this classical result to nonzero sum games, which typically have multiple Nash equilibria and multiple values. Our object is the set value of the game, which roughly speaking is the set of values over all equilibria and thus is by nature unique. We shall introduce set valued Hamiltonians and characterize the set value of the game through backward SDEs driven by appropriate selectors of the set valued Hamiltonians, where the selectors are typically path dependent. When the set valued Hamiltonian is a singleton, our result covers the standard control problem and two person zero sum game problem under Isaacs condition.

math.OC↗