Computational methods for various stochastic differential equation models in finance

Abstract

This study develops efficient numerical methods for solving jumpdiffusion stochastic delay differential equations and stochastic differential equations with fractional order. In addition, two novel algorithms are developed for the estimation of parameters in the stochastic models. One of the algorithms is based on the implementation of the Bayesian inference and the Markov Chain Monte Carlo method, while the other one is developed by using an implicit numerical scheme integrated with the particle swarm optimization.