Description: This paper considers the Bayesian analysis of the generalized Poisson distribution GPD and the generalized Poisson regression GPR model. Markov chain Monte Carlo MCMC methods and random variety generation strategies such as adaptive rejection sampling ARS for log-concave densities and adaptive rejection Metropolis sampling ARMS are discussed and then utilized in order to advance the Bayesian analysis of these generalized Poisson models.

Description: This paper builds a new risk model for a firm which is sensitive to its credit quality. A modified Jarrow, Lando and Turnball model [Markov Chain model] is used to model the credit rating. Recursive equations for finite time ruin probability and distribution of ruin time are derived. Coupled Volterra type integral equation systems for ultimate ruin probability, severity of ruin and joint distribution of surplus before and after ruin are also obtained. Some numerical results are included.