FIRST JUMP TIME IN SIMULATION OF SAMPLING TRAJECTORIES OF AFFINE JUMP-DIFFUSIONS DRIVEN BY alpha-STABLE WHITE NOISE

摘要

The aim of this paper is twofold. Firstly, we derive an explicit expression of the (theoretical) solutions of stochastic differential equations with affine coefficients driven by alpha-stable white noise. This is done by means of Ito formula. Secondly, we develop a detection algorithm for the first jump time in simulation of sampling trajectories which are described by the solutions. The algorithm is carried out through a multivariate Lagrange interpolation approach. To this end, we utilise a computer simulation algorithm in MATLAB to visualise the sampling trajectories of the jump-diffusions for two combinations of parameters arising in the modelling structure of stochastic differential equations with affine coefficients.