  Traditional techniques for calculating outstanding claim liabilities such as
the chain ladder are notoriously at risk of being distorted by outliers in past
claims data. Unfortunately, the literature in robust methods of reserving is
scant, with notable exceptions such as Verdonck and Debruyne (2011) and
Verdonck and Van Wouwe (2011). In this paper, we put forward two alternative
robust bivariate chain-ladder techniques to extend the approach of Verdonck and
Van Wouwe (2011). The first technique is based on Adjusted Outlyingness (Hubert
and Van der Veeken, 2008) and explicitly incorporates skewness into the
analysis whilst providing a unique measure of outlyingness for each
observation. The second technique is based on bagdistance (Hubert et al., 2016)
which is derived from the bagplot however is able to provide a unique measure
of outlyingness and a means to adjust outlying observations based on this
measure.
  Furthermore, we extend our robust bivariate chain-ladder approach to an
N-dimensional framework. The implementation of the methods, especially beyond
bivariate, is not trivial. This is illustrated on a trivariate data set from
Australian general insurers, and results under the different outlier detection
and treatment mechanisms are compared.
