  An intensive research sprang up for stochastic methods in insurance during
the past years. To meet all future claims rising from policies, it is requisite
to quantify the outstanding loss liabilities. Loss reserving methods based on
aggregated data from run-off triangles are predominantly used to calculate the
claims reserves. Conventional reserving techniques have some disadvantages:
loss of information from the policy and the claim's development due to the
aggregation, zero or negative cells in the triangle; usually small number of
observations in the triangle; only few observations for recent accident years;
and sensitivity to the most recent paid claims.
  To overcome these dilemmas, granular loss reserving methods for individual
claim-by-claim data will be derived. Reserves' estimation is a crucial part of
the risk valuation process, which is now a front burner in economics. Since
there is a growing demand for prediction of total reserves for different types
of claims or even multiple lines of business, a time-varying copula framework
for granular reserving will be established.
