arXiv subjects

Neil A. Chriss

Publications and source records attributed to Neil A. Chriss.

4 recordsLinked to original sources

arXiv2025

Position building in competition is a game with incomplete information

This paper examines strategic trading under incomplete information, where firms lack full knowledge of key aspects of their competitors' trading strategies such as target sizes and market impact models. We extend previous work on competitive trading equilibria by incorporating uncertainty through the framework of Bayesian games. This allows us to analyze scenarios where firms have diverse beliefs about market conditions and each other's strategies. We derive optimal trading strategies in this setting and demonstrate how uncertainty significantly impacts these strategies compared to the complete information case. Furthermore, we introduce a novel approach to model the presence of non-strategic traders, even when strategic firms disagree on their characteristics. Our analysis reveals the complex interplay of beliefs and strategic adjustments required in such an environment. Finally, we discuss limitations of the current model, including the reliance on linear market impact and the lack of dynamic strategy adjustments, outlining directions for future research.

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arXiv2024

Optimal position-building strategies in competition

This paper develops a mathematical framework for building a position in a stock over a fixed period of time while in competition with one or more other traders doing the same thing. We develop a game-theoretic framework that takes place in the space of trading strategies where action sets are trading strategies and traders try to devise best-response strategies to their adversaries. In this setup trading is guided by a desire to minimize the total cost of trading arising from a mixture of temporary and permanent market impact caused by the aggregate level of trading including the trader and the competition. We describe a notion of equilibrium strategies, show that they exist and provide closed-form solutions.

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arXiv2024

Competitive equilibria in trading

This is the third paper in a series concerning the game-theoretic aspects of position-building while in competition. The first paper set forth foundations and laid out the essential goal, which is to minimize implementation costs in light of how other traders are likely to trade. The majority of results in that paper center on the two traders in competition and equilibrium results are presented. The second paper, introduces computational methods based on Fourier Series which allows the introduction of a broad range of constraints into the optimal strategies derived. The current paper returns to the unconstrained case and provides a complete solution to finding equilibrium strategies in competition and handles completely arbitrary situations. As a result we present a detailed analysis of the value (or not) of trade centralization and we show that firms who naively centralize trades do not generally benefit and sometimes, in fact, lose. On the other hand, firms that strategically centralize their trades generally will be able to benefit.

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arXiv2024

Position-building in competition with real-world constraints

This paper extends the optimal-trading framework developed in arXiv:2409.03586v1 to compute optimal strategies with real-world constraints. The aim of the current paper, as with the previous, is to study trading in the context of multi-player non-cooperative games. While the former paper relies on methods from the calculus of variations and optimal strategies arise as the solution of partial differential equations, the current paper demonstrates that the entire framework may be re-framed as a quadratic programming problem and cast in this light constraints are readily incorporated into the calculation of optimal strategies. An added benefit is that two-trader equilibria may be calculated as the end-points of a dynamic process of traders forming repeated adjustments to each other's strategy.

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