Calendar Effect and In-Sample Forecasting Applied to Mesothelioma Mortality Data

In this paper, we apply and further illustrate a recently developed extended continuous chain ladder model to forecast mesothelioma deaths. Making such a forecast has always been a challenge for insurance companies as exposure is difficult or impossible to measure, and the latency of the disease usually lasts several decades. While we compare three approaches to this problem, we show that the extended continuous chain ladder model is a promising benchmark candidate for asbestosis mortality forecasting due to its flexible and simple forecasting strategy. Furthermore, we demonstrate how the model can be used to provide an update for the forecast of the number of deaths due to mesothelioma in Great Britain using in recent Health and Safety Executive (HSE) data.

One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model

We investigate the relation between one-year reserve risk and ultimate reserve risk in Mack Chain Ladder model in a simulation study. The first goal is to validate the so-called linear emergence pattern formula, which maps the ultimate loss to the one-year loss, in case when we measure the risks with Value-at-Risk. The second goal is to estimate the true emergence pattern of the ultimate loss, i.e., the conditional distribution of the one-year loss given the ultimate loss, from which we can properly derive a risk measure for the one-year horizon from the simulations of ultimate losses. Finally, our third goal is to test if classical actuarial distributions can be used for modelling of the outstanding loss from the ultimate and the one-year perspective. In our simulation study, we investigate several synthetic loss triangles with various duration of the claims development process, volatility, skewness, and distributional assumptions of the individual development factors. We quantify the reserve risks without and with the estimation error of the claims development factors.

A job ladder model with stochastic employment opportunities

We set up a model with on‐the‐job search in which firms infrequently post vacancies for which workers occasionally apply. The model nests the standard job ladder and stock‐flow models as special cases, while remaining analytically tractable and easy to estimate from standard panel data sets. The parameters from a structurally estimated model on US data are significantly different from either the restrictions imposed by a stock‐flow or job ladder model. Imposing these restrictions significantly understates the search option associated with employment and are, unlike our model, inconsistent with recent survey evidence and declining job finding rates and starting wage with duration of unemployment, both of which are present in the data.

A viscoelastic model for seismic attenuation using fractal mechanical networks

SUMMARY Seismic attenuation (quantified by the quality factor Q) has a significant impact on the seismic waveforms, especially in the fluid-saturated rocks. This dissipative process can be phenomenologically represented by viscoelastic models. Previous seismological studies show that the Q value of Earth media exhibits a nearly frequency-independent behaviour (often referred to as constant-Q in literature) in the seismic frequency range. Such attenuation can be described by the mathematical Kjartansson constant-Q model, which lacks of a physical representation in the viscoelastic sense. Inspired by the fractal nature of the pore fluid distribution in patchy-saturated rocks, here we propose two fractal mechanical network (FMN) models, that is, a fractal tree model and a quasi-fractal ladder model, to phenomenologically represent the frequency-independent Q behaviour. As with the classic viscoelastic models, the FMN models are composed of mechanical elements (spring and dashpots) arranged in different hierarchical patterns. A particular parametrization of each model can produce the same complex modulus as in the Kjartansson model, which leads to the constant-Q. Applying the theory to several typical rock samples, we find that the seismic attenuation signature of these rocks can be accurately represented by either one of the FMN models. Besides, we demonstrate that the ladder model in particular exhibits the realistic multiscale fractal structure of the saturated rocks. Therefore, the FMN models as a proxy could provide a new way to estimate the microscopic rock structure property from macroscopic seismic attenuation observation.

Actuarial Evaluation of Late Losses: A Chain Ladder Model or a Generalized Linear Model of Rated Loss Increaments with a Poisson Distribution?

This article focuses on the equality of the estimated late losses resulting from the application of the chain ladder model to the estimates obtained on the basis of the incremental development triangle by cross-parameterizing the rated increments of losses with Poisson distributions using the generalized linear model. In this article, the formulas of the chain ladder model are derived by solving the problem of cross parameterization of rated increments of losses. Smaller accounting groups than the risk, along which the development triangle is formed, make conclusions about the possible bases for the sharing of reserves. This issue may be relevant for the further calculation of actuarial premiums.