Two essays on multivariate stochastic processes and applications to credit risk modeling.

摘要

This thesis is made up of two essays. In the first essay we study certain aspects of stochastic dependence between some classes of finite dimensional semimartingale processes in terms of their infinitesimal characteristics. We study what are the conditions to be satisfied by the local characteristics of a vector valued semimartingale so that law of its components is the same as the law of a given collection of processes. In the second essay we study two approximations (in distribution) to a class of Markov processes known as diffusion modulated Markov chains. In particular we analyze their so called fluid limit and diffusion approximation and derive some estimates on the approximation error arising from using the fluid limit and diffusion approximations as a proxy of the original process. Both essays are motivated by financial applications, such as valuation and hedging of financial derivatives written on baskets of underlying securities.