  Within the Solvency II framework the insurance industry requires a realistic
modelling of the risk processes relevant for its business. Every insurance
company should be capable of running a holistic risk management process to meet
this challenge. For property and casualty (P&C) insurance companies the risk
adequate modelling of the claim reserves is a very important topic as this
liabilities determine up to 70% percent of the balance sum. We propose a three
dimensional (3D) stochastic model for claim reserving. It delivers consistently
the reserve's distribution function as well as the distributions of all parts
of it that are needed for accounting and controlling. The calibration methods
for the model are well known from data analysis and they are applicable in an
practitioner environment. We evaluate the model numerically by the help of
Monte Carlo (MC) simulation. Classical actuarial reserve models are two
dimensional (2D). They lead to an estimation algorithm that is applied on a 2D
matrix, the run off triangle. Those methods (for instance the Chain - Ladder or
the Bornhuetter - Ferguson method) are widely used in practice nowadays and
give rise to several problems: They estimate the reserves' expectation and some
of them - under very restriction assumptions - the variance. They provide no
information about the tail of the reserve's distribution, what would be most
important for risk calculation, for assessing the insurance company's financial
stability and economic situation. Additionally, due to the projection of the
claim process into a two dimensional space the results are very often distorted
and dependent on the kind of projection. Therefore we extend the classical 2D
models to a 3D space because we find inconsistencies generated by inadequate
projections into the 2D spaces.
