The present paper provides a unif3"ing survey of some of the most important methods and models of loss reserving which are based on run-off triangles. The starting point is the thesis that the use of runoff triangles in loss reserving can be justified only under the assumption that the development of the losses of ever3, accident year follows a development pattern which is common to all acciden...

Modeling the dependence among multiple loss triangles has important implications for the determination of loss reserves, a critical element of risk management and capital allocation practices of property-casualty insurers. In this article, we propose a copula regression model for dependent lines of business that can be used to predict unpaid losses and hence determine loss reserves. The propose...

In this paper we examine the claims reserving problem using Tweedie’s compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated ...

We present a novel stochastic model for claims reserving that allows to combine claims payments and incurred losses information. The main idea is to combine two claims reserving models (Hertig’s model [11] and Gogol’s model [8]) leading to a log-normal paid-incurred chain (PIC) model. Using a Bayesian point of view for the parameter modelling we derive in this Bayesian PIC model the full predic...

This paper shows how expert opinion can be inserted into a stochastic framework for claims reserving. The reserving methods used are the chain-ladder technique and Bornhuetter-Ferguson, and the stochastic framework follows England and Verrall (2062). Although stochastic models have been studied, there are 2 main obstacles to their more frequent use in practice: ease of implementation and adapta...

Continuing research begun in 2], we investigate problems of reserving capacity in the arcs of a network, subject to the constraint that, on the failure of any one arc, there is enough reserved capacity on the remaining arcs to support a ow of value T from a source s to a destination t. We also impose upper bounds on the amount of capacity we may reserve on the arcs: this alters the nature of th...