Some Derivations on Levy and Jump Processes

Abstract

Modeling with jump processes has become an integral part of real life mathematics. Besides actuarial applications jump processes have frequently been applied in credit risk modeling, derivative pricing, interest rate modeling, signal processing and so on. Behind every jump process there always exists a stochastic process. Once this stochastic process satisfies some conditions (to be mentioned) it is known as Lévy process. This particular family of stochastic processes has rich structures of its own which facilitate the study of jump processes associated with the processes belonging to this family. In this article some results, involving both Lévy and jump processes, are proved in details. These details derivations, explicitly showing the intuitive meaning of Lévy properties, are not available in the existing literature.

GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 11-22

DOI: http://dx.doi.org/10.3329/ganit.v29i0.8511