# An FBSDE approach to market impact games with stochastic parameters

@article{Drapeau2019AnFA, title={An FBSDE approach to market impact games with stochastic parameters}, author={Samuel Drapeau and Peng Luo and Alexander Schied and Dewen Xiong}, journal={arXiv: Trading and Market Microstructure}, year={2019} }

We analyze a market impact game between $n$ 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… Expand

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#### References

SHOWING 1-10 OF 26 REFERENCES

A State‐Constrained Differential Game Arising in Optimal Portfolio Liquidation

- Economics, Mathematics
- 2013

We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain… Expand

Algorithmic Trading with Partial Information: A Mean Field Game Approach

- Economics
- 2018

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform… Expand

Predatory Trading : a Game on Volatility and Liquidity

- 2008

We propose and analyze a continuous time stochastic differential game as a mathematical model for the liquidation of a financial position by a distressed trader facing a predator trading with looser… Expand

A Market Impact Game Under Transient Price Impact

- Economics, Computer Science
- Math. Oper. Res.
- 2019

It is proved that for small transaction costs the high-frequency traders engage in a "hot-potato game", in which the same asset position is sold back and forth, and identifies a critical value for the size of the transaction costs above which all oscillations disappear and strategies become buy-only or sell-only. Expand

Optimal Trading with Stochastic Liquidity and Volatility

- Economics, Computer Science
- SIAM J. Financial Math.
- 2012

A Hamilton-Jacobi-Bellman equation is constructed for the optimal cost and strategy of mean-variance optimal agency execution strategies for varying risk aversion and these strategies adapt optimally to the instantaneous variations of market quality. Expand

Optimal trade execution: A mean quadratic variation approach

- Mathematics
- 2012

We propose the use of a mean quadratic variation criteria to determine an optimal trading strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential… Expand

Optimal execution with nonlinear impact functions and trading-enhanced risk

- Economics
- 2003

Optimal trading strategies are determined for liquidation of a large single-asset portfolio to minimize a combination of volatility risk and market impact costs. The market impact cost per share is… Expand

No-dynamic-arbitrage and market impact

- Economics
- 2009

Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship… Expand

A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions

- Mathematics, Computer Science
- SIAM J. Control. Optim.
- 2015

The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is pre-specified and the solution results establish existence, uniqueness and regularity of solution results. Expand

High-Frequency Limit of Nash Equilibria in a Market Impact Game with Transient Price Impact

- Mathematics, Economics
- SIAM J. Financial Math.
- 2017

It is shown that the limiting strategies form a Nash equilibrium for a continuous-time version of the model with $theta$ equal to a certain critical value $\theta^*>0$, and that the corresponding expected costs coincide with the high-frequency limits of the discrete-time equilibrium costs. Expand