Paper: arXiv 2407.10561

Abstract

We study the perfect information Nash equilibrium between a broker and her clients – an informed trader and an uniformed trader. In our model, the broker trades in the lit exchange where trades have instantaneous and transient price impact with exponential resilience, while both clients trade with the broker. The informed trader and the broker maximise expected wealth subject to inventory penalties, while the uninformed trader is not strategic and sends the broker random buy and sell orders. We characterise the Nash equilibrium of the trading strategies with the solution to a coupled system of forward-backward stochastic differential equations (FBSDEs). We solve this system explicitly and study the effect of information, profitability, and inventory control in the trading strategies of the broker and the informed trader.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper heavily employs advanced mathematical concepts including forward-backward stochastic differential equations (FBSDEs) and matrix Riccati differential equations to characterize the Nash equilibrium, resulting in a high math complexity score. In contrast, it lacks code, statistical metrics, or backtesting details, relying instead on theoretical derivations and generic simulations, which gives it a low empirical rigor score.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Nash Equilibrium between Broker & Clients"] --> B["Key Methodology:<br>Forward-Backward SDEs (FBSDE)"]
  B --> C["Model Setup:<br>Broker, Informed &<br>Uninformed Traders"]
  C --> D["Market Assumption:<br>Transient Price Impact with<br>Exponential Resilience"]
  C --> E["Client Behavior:<br>Informed (Optimal) vs.<br>Uninformed (Random)"]
  D & E --> F["Computational Process:<br>Derive Coupled FBSDE System"]
  F --> G["Solution Strategy:<br>Explicit Closed-Form<br>Nash Equilibrium"]
  G --> H["Key Findings:<br>Equilibrium Strategies,<br>Impact of Info, Profit, Inventory"]

Cited References (47)

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  3. Algorithmic market making in dealer markets with hedging and market impact (2023)
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  5. Internalisation by electronic FX spot dealers (2019)
  6. A mean-field game of market-making against strategic traders (2023)
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  8. On the impossibility of informationally efficient markets (1980)
and 39 more
  1. Liquidity and market structure (1988)
  2. Unwinding Toxic Flow with Partial Information — → 2407.04510
  3. Detecting toxic flow — → 2312.05827
  4. Unwinding Stochastic Order Flow: When to Warehouse Trades — → 2310.14144
  5. Double-execution strategies using path signatures (2022)
  6. Trading foreign exchange triplets (2020)
  7. A Mean Field Game between Informed Traders and a Broker — → 2401.05257
  8. A survey of nonsymmetric Riccati equations (2002)
  9. Non—Blow—Up Conditions for Riccati—type Matrix Differential and Difference Equations (2000)
  10. Optimal signal-adaptive trading with temporary and transient price impact (2022)
  11. Optimal trading: The importance of being adaptive (2021)
  12. Mean-field games with differing beliefs for algorithmic trading (2020)
  13. Trading algorithms with learning in latent alpha models (2019)
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5 of 47 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.