Bayesian statistics and the Monte Carlo method

We discuss the application of the Bayesian statistical paradigm in conjunction with Monte Carlo methods to practical problems. We begin by describing the basic constructs of the Bayesian paradigm. We then discuss two applications. The first entails the simulation of a two-stage model of a property-casualty insurance operation. The second application simulates the operation of an insurance regime for home equity conversion mortgages (also known as reverse mortgages). In this simulation, we built separate models to (1) predict the appreciation of individual home values and (2) predict the annual mortality experience of individual insureds. A feature of this work was the simulation of the parameters of these models in order to explicitly incorporate their variability into the model. We conclude the work by considering (1) model validation issues and (2) alternate forms of scenario testing - i.e., those employing pseudorandom numbers, quasi-random numbers, or even more subjective schemes.