Год выпуска: 2010 Автор: Terry Lynch and John Appleby Издательство: LAP Lambert Academic Publishing Страниц: 240 ISBN: 9783843359351
Описание
This monograph deals with the asymptotic behaviour, and in particular the largest fluctuations, of various classes of stochastic differential equations (SDEs) and their discretisations. Equations subject to Markovian switching are also studied, allowing the drift and diffusion coefficients to switch randomly according to a Markov jump process. The assumptions are motivated by the large fluctuations experienced by financial markets which are subjected to random regime shifts. Such results are then applied to a variant of the classical Geometric Brownian Motion (GBM) market model. Moreover it is shown that discrete approximations to these equations, using standard and split-step implicit Euler-Maruyama methods, exhibit asymptotic behaviour which is consistent with their continuous-time counterparts.
