We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2018)  , who considered two agents and one asset , we focus our attention on the conditions on the value of transaction cost making the trading profile of the agents, and as a consequence the price trajectory, wildly oscillating and the market unstable. We  find that the presence of more assets , the heterogeneity of trading skills (e.g. speed or cost), and a large number of agents make the market more prone to large oscillations and instability. When the number of assets is fixed, a more complex structure of the cross-impact matrix, i.e. the existence of multiple factors for liquidity, makes the market less stable compared to the case when a single liquidity factor exists.
We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2018) and Luo and Schied (2020) , who considered the one asset case , we focus our attention on the conditions on the value of transaction cost making the trading profile of the agents, and as a consequence the price trajectory, wildly oscillating and the market unstable. We prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We find that the presence of more assets and a large number of agents make the market more prone to large oscillations and instability. When the number of assets is fixed, a more complex structure of the cross-impact matrix, i.e. the existence of multiple factors for liquidity, makes the market less stable compared to the case when a single liquidity factor exists.
A
and Luo and Schied (2020)
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two agents and one asset
the one asset case
A
prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We
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, the heterogeneity of trading skills (e.g. speed or cost),