One of the main tasks of non-life actuaries is to predict the outstanding loss liabilities. This prediction is called claims reserves and it should suffice to settle all open claims. These claims reserves are, on the one hand, an important basis for premium calculations and, on the other hand, they have a decisive impact on the profit and loss account, as they constitute the biggest financial position on the liability side of a non-life insurance company's balance sheet. An adverse claims development is also the biggest insurance risk for solvency considerations. Therefore, it is very important to have accurate claims reserves and precise information about the uncertainties in these claims reserves.

In the lectures we consider "Stochastic Claims Reserving Methods in Insurance" which exactly copes with the issues of having accurate claims reserves and information about their uncertainties. Our focus will be on methods and techniques relevant for practice. First we treat several well-known methods such as the chain ladder method and the Bornhuetter-Ferguson method, but together with the corresponding underlying stochastic models and including the estimators for the mean square error of prediction. In addition we will also present new methods such as the paid-incurred chain method. With regard to the reserve uncertainty, we will treat the classical view of the "ultimate" reserve risk as well as the recently emerged "one-year" reserve risk needed for solvency purposes and leading to the cost-of-capital loading. The lectures are complemented by computer exercises, for which no prerequisite knowledge is needed.

 - Introduction to claims reserving
 - Chain ladder method (classical and Bayesian model)
 - Bornhuetter-Ferguson, Cape-Cod and loss-ratio methods
 - Over-dispersed Poisson and generalized linear model methods
 - Paid-incurred chain method
 - Simulation techniques such as bootstrap and Markov chain Monte Carlo method
 - One-year view, claims development result and cost-of-capital loading for the runoff

Target audience: students and researchers with a good general knowledge of probability and statistics as well as practicing actuaries.

Oral exam at Prof. Uwe Schmock