SIMULATION OF AN INTEGRO-DIFFERENTIAL EQUATION AND APPLICATION IN ESTIMATION OF RUIN PROBABILITY WITH MIXED FRACTIONAL BROWNIAN MOTION

摘要

We consider the numerical solution of one type of integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we try to simulate the estimation of ruin probability with an unknown parameter driven not by the classical Levy process, but by the mixed fractional Brownian motion.