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.