Abstract by Cason Wight
Error Bounds for Solutions to Continuous Time Semi-Markov Models
Semi-Markov processes effectively model waiting times and probabilities in scenarios with multiple states. One example is auto-insurance companies categorizing drivers to a specific risk level (“preferred risk”, “high risk”, etc.) using the bonus-malus system. The question of error bounds for solutions in discrete models has been answered. The error bounds when solving continuous time processes has not been found. A fast and effective method of obtaining solutions in semi-Markov models is the Discrete Fourier-Transform (DFT). Using the DFT for solutions to continuous models introduces two types of errors. The first type is discretization error, which occurs when computing a continuous process at discrete points. The other is truncation error, which is introduced when eliminating the tail of an infinite distribution for computational purposes. The research goal is to find the error bounds involved in computing solutions to continuous time semi-Markov models.