Abstract:

In Mathematical Finance the price process is a risky asset is usually modelled by the trajectory of a stochastic process on some underlying probability space. Since asset prices are generated by the demand of agents who are active on a financial market, stock prices should be viewed as the result of an interaction between many agents with possibly bounded rationality. If the number of market participants involved in the formation of stock prices becomes large, such an approach allows to bring in techniques from Markov random field theory, from the theory of interacting Markov processes or from queueing theory. In this talk we review some recent results on the mathematical modelling of market microstructure. In particular, we study the impact of investor inertia on the dynamics of stock prices.