MC 6460
Speaker
ÌýPeng LuoÌý| Department of Statistics and Actuarial Science, University of À¶Ý®ÊÓƵ
Title
An FBSDE approach to market impact games with stochasticÌýparameters
Abstract
Market impact refers to the fact that the execution of a large order influences the price of the underlying asset.Ìý The phenomenon of price impact becomes relevant for orders that are large in comparison to the instantaneously available liquidity in markets.Ìý Market impact games analyze situations in which several agents compete for liquidity in a market impact model or try to exploit the price impact generated by competitors. In this talk I willÌýanalyze a market impact game between severalÌýrisk averse agents whoÌýcompete for liquidity in a market impact model with permanent priceÌýÌýimpact and additional slippage. Most market parameters, includingÌývolatility and drift, are allowed to vary stochastically. The first mainÌýresult characterizes the Nash equilibrium in terms of a fully coupledÌýsystem of forward-backward stochastic differential equations (FBSDEs). TheÌýsecond main result provides conditions under which this system ofÌýFBSDEs has indeed a unique solution, which in turn yields the uniqueÌýNash equilibrium. Closed-form solutions are obtained in specialÌýsituations and numerical results are provided.