Discrete-Time Risk Processes with After-Effects and Association

Abstract

We present a simple discrete-time model of a risk process in which primary claims are followed by secondary claims representing after-effects. It is shown that the resulting discrete-time process is associated. Estimates for finite and infinite horizon ruin probabilities are then obtained via a diffusion approximation that is based on the classic Functional Central Limit Theorem of Newman and Wright (1981) for sequences of associated random variables.

Analysis of a Multivariate Claim Process

“…In credit risk analysis, Herbertsson (2011) uses multivariate phase-type distributions to model default contagion in credit risk. Some other developments can be found in Rabehasaina (2009) and Zaphiropoulos and Zazanis (2010).…”