Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models

This research proposes a mortality model with an age shift to project future mortality using principal component analysis (PCA). Comparisons of the proposed PCA model with the well-known models—the Lee-Carter model, the age-period-cohort model (Renshaw and Haberman, 2006), and the Cairns, Blake, and Dowd model—employ empirical studies of mortality data from six countries, two each from Asia, Europe, and North America. The mortality data come from the human mortality database and span the period 1970-2005. The proposed PCA model produces smaller prediction errors for almost all illustrated countries in its mean absolute percentage error. To demonstrate longevity risk in annuity pricing, we use the proposed PCA model to project future mortality rates and analyze the underestimated ratio of annuity price for whole life annuity and deferred whole life annuity product respectively. The effect of model risk on annuity pricing is also investigated by comparing the results from the proposed PCA model with those from the LC model. The findings can benefit actuaries in their efforts to deal with longevity risk in pricing and valuation.     

A state‐dependent Markov‐modulated mechanism for generating events and stochastic models

In this paper, we introduce a versatile block‐structured state‐dependent event (BSDE) approach that provides a methodological tool to construct non‐homogeneous Markov‐modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state‐dependent quasi‐birth‐and‐death process that gives a constructive generalization of the scalar birth‐and‐death process and the homogeneous quasi‐birth‐and‐death process. Copyright © 2009 John Wiley & Sons, Ltd.     

Dispersive Blow-Up Ⅱ.Schr(o)dinger-Type Equations,Optical and Oceanic Rogue Waves

Addressed here is the occurrence of point singularities which owe to the fo-cusing of short or long waves,a phenomenon labeled dispersive blow-up.The context of this investigation is linear and nonlinear,strongly dispersive equations or systems of equa-tions.The present essay deals with linear and nonlinear Schr(o)dinger equations,a class of fractional order SchrSdinger equations and the linearized water wave equations,with and without surface tension. Commentary about how the results may bear upon the formation of rogue waves in fluid and optical environments is also included.     

Stochastic Fractional Anderson Models with Fractional Noises

The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

An existence result for elliptic partial differential-algebraic equations arising in semiconductor modeling

We consider a system of partial differential-algebraic equations which model an electric network containing semiconductor devices. The zero-dimensional differential-algebraic network equations are coupled with multi-dimensional elliptic partial differential equations which model the devices. For this coupled system we prove an existence result.     

Empfehlungen zum Gebrauch einheitlicher Halbwertzeiten einiger wichtiger Radionuklide

The present work represents the results of angular distribution measurements performed for promt gamma-rays in the range of 1.1 … 1.2. MeV due to the ²³³U(n, f) and ²³⁹Pu(n,f) reactions. The measurements yielded anisotropy values found to be consistent with values previously measured and using the same technique at different gamma energy bands. Such consistency, also found to exist between anisotropy values previously measured for the ²³⁵U(n,f) reaction, is a strong evidence about the energy independence of the anisotropy and indicates that the gamma spectra (at 180° and 90° to the fission direction) are essentially the same. The average values of the fragment angular momentum were calculated according to Strutinsky and Nix-Swiatecki theories. It was found that the values of the average angular momentum calculated for ²³⁴U, ²³⁶U and ²⁴⁰Pu according to Strutinsky,s formula (at different gamma energy bands) are consistent and yield average values which are in good agreement with those obtained from direct measurements.     

Ein tragbares Kontrollgerät fÜr α-Oberflächenkontaminationen

Es wird ein volltransistorisiertes, tragbares Gerät zur Bestimmung von a-Oberflächenkontaminationen beschrieben, welches mit 7 Proportionahählrohren VA-Z-520 arbeitet. Ein mechanisches Zählwerk dient zur Verbesserung der Anzeige bei kleinen Aktivitätswerten, bei gröβeren erfolgt diese durch ein Ratemeter. Die laut Strahlenschutzverordnung zulässigen α-Oberflächenkontaminationen können mit diesem Gerät kontrolliert werden. Die Kalibrierung wurde mit Hilfe eines ²³⁹Pu-Standardflächenpräparates ausgeführt. Das Gerät ist auβerdem für β-γ-Messungen geeignet. Hierzu wird lediglich der Zählrohrteil der Sonde gegen den β-γ-Kopf mit 7 Stück VA-Z-310 ausgetauscht.     

Isotopengeochemisches Kompartimentmodell des Stickstoffkreislaufs

Es wird ein Modell des globalen Kreislaufs des Stickstoffs und seiner Isotope beschrieben, das die folgenden geochemischen Reservoire berücksichtigt: Stickstoff in Magmatiten, Stickstoff in Metamorphiten, Stickstoff in Sedimentiten und Stickstoff der Atmosphäre. Das Modell berücksichtigt den Stickstoffaustausch zwischen Magmatiten und dem Oberen Mantel, den Übergang des Stickstoffs aus Magmatiten und Metamorphiten in die Atmosphäre und den Stickstoffaustausch zwischen Sedimentiten und der Atmosphäre und andere geochemische Prozesse.

Auf der Grundlage aller gegenwärtig zugänglichen δ¹⁵N-Werte magmatischer, metamorpher und sedimentärer Gesteine und plausibler Annahmen über die Isotopieeffekte, die bei der Bildung dieser Stickstoffflüsse wirken, werden – unter Benutzung des mathematischen Formalismus der Kompartimenttheorie – quantitative Aussagen abgeleitet über das Ausmaß des Stickstoffaustausches zwischen der Erdkruste und dem Oberen Mantel und über andere Stickstoffflüsse, die den globalen Stickstoffkreislauf charakterisieren.     

Characterising ontogenetic niche shifts in Nile crocodile using stable isotope (δ13C, δ15N) analyses of scute keratin

Nile crocodiles undergo a three to five order of magnitude increase in body size during their lifespan. This shift coincides with a change in resource and habitat use which influences the strength, type and symmetry of interactions with other species. Identifying size-specific crocodile groups displaying similar traits is important for conservation planning. Here, we illustrate how stable carbon (δ¹³ C) and nitrogen (δ¹⁵ N) isotope analysis of scute keratin, together with breakpoint modelling analysis can be used to characterise ontogenetic niche shifts. Using a sample set of 238 crocodiles from the Okavango Delta, Botswana (35–463 cm total length), we found prominent size-related changes in the scute keratin δ¹³ C and δ¹⁵ N profiles close to 40 and 119 cm snout-vent length. The first shift corroborated the findings of a traditional stomach-content study conducted on the same population at the same time, and the second conformed to known crocodile ecology. This approach can be used as a first approximation to identify size-specific groups within crocodile populations, and these can then be investigated further using isotopic or other methods.