Market Impact Models

Classical models of Financial Mathematics assume that the evolution of the prices of financial assets is prescribed exogenously via given stochastic processes and it is not affected by the investment decisions of market participants. Financial Economics, on contrary, derives prices from equilibrium, in which the participants interact through their trading activity. Recently, a middle-ground approach became popular (among academics and practitioners). This approach allows the prices to depend on trading activity, implying that they cannot be fixed exogenously, but does not require one to go through the full (usually complicated) equilibrium construction, to find the exact dependence of the prices on the trading activity. This is what is often referred to as the Market Impact models. I will present a survey of existing results in this area and will discuss my contributions in more detail.