Given a Bayesian Markov chain Monte Carlo (MCMC) stochastic loss reserve model for two separate lines of insurance, this paper describes how to fit a bivariate stochastic model that captures the dependencies between the two lines of insurance. A Bayesian MCMC model similar to the Changing Settlement Rate (CSR) model, as described in Meyers (2015), is initially fit to each line of insurance. Then taking a sample from the posterior distribution of parameters from each line, this paper shows how to produce a sample that represents a bivariate distribution that maintains the original univariate distributions as its marginal distributions. This paper goes on to compare the predicted distribution of outcomes by this model with the actual outcomes, and a bivariate model predicted under the assumption that the lines are independent. It then applies two Bayesian model selection statistics to compare the fits of the two models.
