Conditional least squares and copulae in claims reserving for a single line of business

•A time series model for the conditional mean and variance of the claims.•The time series innovations for the consecutive claims not to be independent.•Conditional least squares to estimate model parameters and consistency proved.•A copula approach for modeling the dependence structure.•A semiparametric bootstrap to estimate the distribution of the reserves.

One of the main goals in non-life insurance is to estimate the claims reserve distribution. A generalized time series model, that allows for modeling the conditional mean and variance of the claim amounts, is proposed for the claims development. On contrary to the classical stochastic reserving techniques, the number of model parameters does not depend on the number of development periods, which leads to a more precise forecasting.Moreover, the time series innovations for the consecutive claims are not considered to be independent anymore. Conditional least squares are used to estimate model parameters and consistency of these estimates is proved. The copula approach is used for modeling the dependence structure, which improves the precision of the reserve distribution estimate as well.Real data examples are provided as an illustration of the potential benefits of the presented approach.