The estimation of phase-type related functionals using Markov chain Monte Carlo methods

In this paper we present a method for estimation of functionals depending on one or several phase-type distributions. This could for example be the ruin probability in a risk reserve process where claims are assumed to be of phase-type. The proposed method uses a Markov chain Monte Carlo simulation to reconstruct the Markov jump processes underlying the phase-type variables in combination with Gibbs sampling to obtain a stationary sequence of...