Probability measure-valued jump-diffusions in finance and related topics
No TL;DR found
Abstract
The martingale problem is known to be a classical and very powerful technology for the study of Markov processes through the analytical properties of the corresponding generators. This approach permits for instance to easily model Markov processes featuring both diffusion and jump components. The first aim of the thesis is to develop concrete and easy–to–use tools allowing to employ this technology in the context of probability measure-valued jump-diffusions. This is mainly motivated by our second line of research, consisting in the study of the so–called polynomial jump-diffusions, which have found broad applications in mathematical finance. However, we will also show that the same tools can be used in much greater generality. Given a linear operator G playing the role of the generator, the martingale problem asks for a process X := (Xt)t≥0, called jump-diffusion, such that p(Xt)− ∫ t