Multiplicative local linear hazard estimation and best one-sided cross-validation

This paper develops detailed mathematical statistical theory of a new class of cross-validation techniques of local linear kernel hazards and their multiplicative bias corrections. The new class of cross-validation combines principles of local information and recent advances in indirect cross-validation. A few applications of cross-validating multiplicative kernel hazard estimation do exist in the literature. However, detailed mathematical statistical theory and small sample performance are introduced via this paper and further upgraded to our new class of best one-sided cross-validation. Best one-sided cross-validation turns out to have excellent performance in its practical illustrations, in its small sample performance and in its mathematical statistical theoretical performance

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

In-Sample Forecasting Applied to Reserving and Mesothelioma Mortality

This paper shows that recent published mortality projections with unobserved exposure can be understood as structured density estimation. The structured density is only observed on a sub-sample corresponding to historical calendar time. The mortality forecast is obtained by extrapolating the structured density to future calendar times using that the components of the density are identified within sample. The new method is illustrated on the important practical problem of forecasting mesothelioma for the UK population. Full asymptotic theory is provided. The theory is given in such generality that it also introduces mathematical statistical theory for the recent continuous chain ladder model. This allows a modern approach to classical reserving techniques used every day in any non-life insurance company around the globe. Applications to mortality data and non-life insurance data are provided along with relevant small sample simulation studies

A simple benchmark for mesothelioma projection for Great Britain

Background: It is of considerable interest to forecast the future burden of mesothelioma mortality. Data on deaths are available, whereas no measure of asbestos exposure is available. Methods: We compare two Poisson models: a response-only model with an age-cohort specification and a multinomial model with epidemiologically motivated frequencies. Results: The response-only model has 5% higher peak mortality than the dose-response model. The former performs slightly better in out-of-sample comparison. Conclusion: Mortality is predicted to peak at about 2100 deaths around 2017 among males in cohorts until 1966 and below 90 years of age. The response-only model is a simple benchmark that forecasts just as well as more complicated models

Statistical modelling and forecasting of outstanding liabilities in non-life insurance

Non-life insurance companies need to build reserves to meet their claims liability cash flows. They often work with aggregated data. Recently it has been suggested that better statistical properties can be obtained when more aggregated data is available for the statistical analysis than just the classical aggregated payments. When also the aggregated number of claims is available one can define a full statistical model of the nature of the number of claims, their delay until payment and the nature of these payments. In this paper we provide a new development in this direction by entering yet another set of aggregated data, namely the number of payments and when they occurred. A new element of our statistical analysis is that we are able to incorporate inflationary trends of payments in a direct and explicit way. Our new method is illustrated on a real life data set and the conclusion are informative and useful

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

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

Reproductive Biology of the Opossum Pipefish, Microphis brachyurus lineatus, in Tecolutla Estuary, Veracruz, Mexico

The reproductive biology of the opossum pipefish, Microphis brachyurus lineatus, was investigated in Tecolutla estuary, Veracruz, Mexico, to determine sex ratio, size at maturity, gonadal and brood pouch histology, reproductive seasonality, and fecundity of this little-known syngnathid. A total of 345 fish were collected between 1995–1998, with an overall sex ratio of 1:1.35 favoring females. Brooding males made up 45% of the population, resulting in an operational sex ratio of 1:2.45 heavily favoring females. All males \u3e 90 mm SL were considered sexually mature, as this was the size at which the brood pouch was clearly developed. Females \u3e 110 mm SL were sexually mature, and had asynchronous oocyte development. Opossum pipefish appear to have a year-round reproductive season in Tecolutla estuary, as females with vitellogenic oocytes and males with eggs in the brood pouch were captured during every month of the year. The number of eggs in the brood pouch was positively correlated with male SL (P \u3c 0.001), and in all but 2 cases males brooded embryos from a single female. The brood pouch is not enclosed by a membrane, and each egg is embedded in a septum consisting of epithelial tissue and numerous blood vessels. Evidence from this study suggests M. brachyurus lineatus may be a sequentially polygamous species with sex-role reversal reproductive behavior, although additional research is necessary to confirm the reproductive ecology and behavior of the species