Shot-noise processes and the minimal martingale measure

Abstract

This article proposes a model for stock prices which incorporates shot-noise effects. This means, that sudden jumps in the stock price are allowed, but their effect may decline as time passes by. Our model is general enough to capture arbitrary effects of this type. Generalizing previous approaches to shot noise we in particular allow the decay to be stochastic. This model describes an incomplete market, so that the martingale measure is not unique. We derive the minimal martingale measure via continuous time methods.