An FBSDE approach to market impact games with stochastic parameters
Samuel Drapeau, Peng Luo, Alexander Schied, Dewen Xiong
TL;DR
This paper models a market impact game with stochastic parameters among risk-averse agents, characterizing the Nash equilibrium through coupled FBSDEs and establishing conditions for uniqueness, with analytical and numerical solutions.
Contribution
It introduces a novel FBSDE framework for analyzing market impact games with stochastic parameters and provides conditions for the existence and uniqueness of equilibrium solutions.
Findings
Characterization of Nash equilibrium via coupled FBSDEs
Conditions for unique solutions to the FBSDE system
Closed-form solutions in special cases and numerical analysis
Abstract
We analyze a market impact game between risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has indeed a unique solution, which in turn yields the unique Nash equilibrium. We furthermore obtain closed-form solutions in special situations and analyze them numerically
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