Double Chain Ladder

By adding the information of reported count data to a classical triangle of reserving data, we derive a suprisingly simple method for forecasting IBNR and RBNS claims. A simple relationship between development factors allows to involve and then estimate the reporting and payment delay. Bootstrap methods provide prediction errors and make possible the inference about IBNR and RBNS claims, separately

Validating the double chain ladder stochastic claims reserving model

Double chain ladder, introduced by Martínez-Miranda et al. (2012), is a statistical model to predict outstanding claim reserve. Double chain ladder and Bornhuetter-Ferguson are extensions of the originally described double chain ladder model which gain more stability through including expert knowledge via an incurred claim amounts triangle. In this paper, we introduce a third method, the incurred double chain ladder, which replicates the popular results from the classical chain ladder on incurred data. We will compare and validate these three using two data sets from major property and casualty insurers

Double Chain Ladder and Bornhuetter-Ferguson

In this article we propose a method close to Double Chain Ladder (DCL) introduced by Martínez-Miranda, Nielsen, and Verrall (2012a). The proposed method is motivated by the potential lack of stability of the DCL method (and of the classical Chain ladder method [CLM] itself). We consider the implicit estimation of the underwriting year inflation in the CLM method and the explicit estimation of it in DCL. This may represent a weak point for DCL and CLM because the underwriting year inflation might be estimated with significant uncertainty. A key feature of the new method is that the underwriting year inflation can be estimated from the less volatile incurred data and then transferred into the DCL model. We include an empirical illustration that illustrates the differences between the estimates of the IBNR and RBNS cash flows from DCL and the new method. We also apply bootstrap estimation to approximate the predictive distributions

Reversible jump Markov chain Monte Carlo method for parameter reduction in claims reserving

We present an application of the reversible jump Markov chain Monte Carlo (RJMCMC) method to the important problem of setting claims reserves in general insurance business for the outstanding loss liabilities. A measure of the uncertainty in these claims reserves estimates is also needed for solvency purposes. The RJMCMC method described in this paper represents an improvement over the manual processes often employed in practice. In particular, our RJMCMC method describes parameter reduction and tail factor estimation in the claims reserving process, and, moreover, it provides the full predictive distribution of the outstanding loss liabilities

Continuous Chain Ladder: Reformulating and generalizing a classical insurance problem

The single most important number in the accounts of a non-life insurance company is likely to be the estimate of the outlying liabilities. Since non-life insurance is a major part of our financial industry (amounting to up to 5% of BNP in western countries), it is perhaps surprising that mathematical statisticians and experts of operational research (the natural experts of the underlying problem) have left the intellectual work on estimating this number to actuaries. This paper establishes this important problem in a vocabulary accessible to experts of operations research and mathematical statistics and it can be seen as an open invitation to these two important groups of scholars to join this research. The paper introduces a number of new methodologies and approaches to estimating outstanding liabilities in non-life insurance. In particular it reformulates the classical actuarial technique as a histogram type of approach and improves this classical technique by replacing this histogram by a kernel smoother

Data collection on trafficking in human beings in the EU: Final report

Trafficking in human beings is the buying and selling of women, girls, men, and boys. It has hugely deleterious consequences for individuals, society, and the economy. This is the fourth report published by the European Commission that presents a compilation of statistics at the EU Member State level on trafficking in human beings. This data collection exercise approached all 28-Member States and covers the years 2015 and 2016and updates the 2014 data collection as relevant

Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers

In this paper we develop a full stochastic cash flow model of outstanding liabilities for the model developed in Verrall, Nielsen and Jessen (2010). This model is based on the simple triangular data available in most non-life insurance companies. By using more data, it is expected that the method will have less volatility than the celebrated chain ladder method. Eventually, our method will lead to lower solvency requirements for those insurance companies that decide to collect counts data and replace their conventional chain ladder method

Parameter Reduction in Log-normal Chain-ladder Models

Multiplicative chain-ladder (CL) models are characterized by CL factors that explain the development of claims from one period to the next. In classical CL models every development period has its own CL factor. In the present paper we give a method describing how some of these CL factors can be modeled by a joint functional dependence. This joint functional form reduces the number of model parameters needed

Methylated DNA recognition during the reversal of epigenetic silencing is regulated by cysteine and cerine residues in the Epstein-Barr Virus lytic switch protein

Epstein-Barr virus (EBV) causes infectious mononucleosis and is associated with various malignancies, including Burkitt's lymphoma and nasopharyngeal carcinoma. Like all herpesviruses, the EBV life cycle alternates between latency and lytic replication. During latency, the viral genome is largely silenced by host-driven methylation of CpG motifs and, in the switch to the lytic cycle, this epigenetic silencing is overturned. A key event is the activation of the viral BRLF1 gene by the immediate-early protein Zta. Zta is a bZIP transcription factor that preferentially binds to specific response elements (ZREs) in the BRLF1 promoter (Rp) when these elements are methylated. Zta's ability to trigger lytic cycle activation is severely compromised when a cysteine residue in its bZIP domain is mutated to serine (C189S), but the molecular basis for this effect is unknown. Here we show that the C189S mutant is defective for activating Rp in a Burkitt's lymphoma cell line. The mutant is compromised both in vitro and in vivo for binding two methylated ZREs in Rp (ZRE2 and ZRE3), although the effect is striking only for ZRE3. Molecular modeling of Zta bound to methylated ZRE3, together with biochemical data, indicate that C189 directly contacts one of the two methyl cytosines within a specific CpG motif. The motif's second methyl cytosine (on the complementary DNA strand) is predicted to contact S186, a residue known to regulate methyl-ZRE recognition. Our results suggest that C189 regulates the enhanced interaction of Zta with methylated DNA in overturning the epigenetic control of viral latency. As C189 is conserved in many bZIP proteins, the selectivity of Zta for methylated DNA may be a paradigm for a more general phenomenon