Nonlinear Normal Correlated Loss Array: Integrated Financial Modeling of Portfolio and Runoff Risk

The runoff triangle is viewed as an incompletely observed rectangular array which also may comprise future loss years. Together with multivariate normality, a parametric structure for the means and covariances completes the stochastic specification. The payment pattern is a core aspect. After maximum likelihood estimation and incorporation of estimation uncertainty, the predictive distribution of the unobserved entities is derived. This distribution is conditional on the observed history and marginal with respect to the estimated parameters. Besides predictive means, also percentiles can be derived. The latter become important when objectifying prudent provisions as well as solvency margins.

Keywords: incurred not settled, covered not incurred, autocorrelation, (negative) multinomial, distributed lag, selection matrix, maximum likelihood, estimation uncertainty, prudent provision, solvency margin.