Individual Loss Reserving with the Multivariate Skew Normal Model

Individual Loss Reserving with the Multivariate Skew Normal Distribution

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses d...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Sarmanov Family of Bivariate Distributions for Multivariate Loss Reserving Analysis

The correlation among multiple lines of business plays a critical role in aggregating claims and thus determining loss reserves for an insurance portfolio. We show that the Sarmanov family of bivariate distributions is a convenient choice to capture the dependencies introduced by various sources, including the common calendar year, accident year and development period effects. The density of th...

Shape mixtures of multivariate skew-normal distributions

Classes of shape mixtures of independent and dependent multivariate skew-normal distributions are considered and some of their main properties are studied. If interpreted from a Bayesian point of view, the results obtained in this paper bring tractability to the problem of inference for the shape parameter, that is, the posterior distribution can be written in analytic form. Robust inference fo...

Multivariate extremes of generalized skew-normal distributions

We explore extremal properties of a family of skewed distributions extended from the multivariate normal distribution by introducing a skewing function π . We give sufficient conditions on the skewing function for the pairwise asymptotic independence to hold. We apply our results to a special case of the bivariate skew-normal distribution and finally support our conclusions by a simulation stud...