Stochastic demography and the neutral substitution rate in class-structured populations.

The neutral rate of allelic substitution is analyzed for a class-structured population subject to a stationary stochastic demographic process. The substitution rate is shown to be generally equal to the effective mutation rate, and under overlapping generations it can be expressed as the effective mutation rate in newborns when measured in units of average generation time. With uniform mutation rate across classes the substitution rate reduces to the mutation rate.

Stochastic time-concentration activity models for cytotoxicity in 3D brain cell cultures.

BACKGROUND: In vitro aggregating brain cell cultures containing all types of brain cells have been shown to be useful for neurotoxicological investigations. The cultures are used for the detection of nervous system-specific effects of compounds by measuring multiple endpoints, including changes in enzyme activities. Concentration-dependent neurotoxicity is determined at several time points. METHODS: A Markov model was set up to describe the dynamics of brain cell populations exposed to potentially neurotoxic compounds. Brain cells were assumed to be either in a healthy or stressed state, with only stressed cells being susceptible to cell death. Cells may have switched between these states or died with concentration-dependent transition rates. Since cell numbers were not directly measurable, intracellular lactate dehydrogenase (LDH) activity was used as a surrogate. Assuming that changes in cell numbers are proportional to changes in intracellular LDH activity, stochastic enzyme activity models were derived. Maximum likelihood and least squares regression techniques were applied for estimation of the transition rates. Likelihood ratio tests were performed to test hypotheses about the transition rates. Simulation studies were used to investigate the performance of the transition rate estimators and to analyze the error rates of the likelihood ratio tests. The stochastic time-concentration activity model was applied to intracellular LDH activity measurements after 7 and 14 days of continuous exposure to propofol. The model describes transitions from healthy to stressed cells and from stressed cells to death. RESULTS: The model predicted that propofol would affect stressed cells more than healthy cells. Increasing propofol concentration from 10 to 100 μM reduced the mean waiting time for transition to the stressed state by 50%, from 14 to 7 days, whereas the mean duration to cellular death reduced more dramatically from 2.7 days to 6.5 hours. CONCLUSION: The proposed stochastic modeling approach can be used to discriminate between different biological hypotheses regarding the effect of a compound on the transition rates. The effects of different compounds on the transition rate estimates can be quantitatively compared. Data can be extrapolated at late measurement time points to investigate whether costs and time-consuming long-term experiments could possibly be eliminated.

Arrested kinetic Li isotope fractionation at the margin of the llimaussaq complex, South Greenland: Evidence for open-system processes during final cooling of peralkaline igneous rocks

Li contents [Li] and isotopic composition (delta Li-7) of mafic minerals (mainly amphibole and clinopyroxene) from the alkaline to peralkaline Ilimaussaq plutonic complex, South Greenland, track the behavior of Li and its isotopes during magmatic differentiation and final cooling of an alkaline igneous system. [Li] in amphibole increase from < 10 ppm in Caamphiboles of the least differentiated unit to >3000 ppm in Na-amphiboles of the highly evolved units. In contrast, [Li] in clinopyroxene are comparatively low (<85 ppm) and do not vary systematically with differentiation. The distribution of Li between amphibole and pyroxene is controlled by the major element composition of the minerals (Ca-rich and Na-rich, respectively) and changes in oxygen fugacity (due to Li incorporation via coupled substitution with ferric iron) during magmatic differentiation. delta(7) Li values of all minerals span a wide range from + 17 to - 8 parts per thousand, with the different intrusive units of the complex having distinct Li isotopic systematics. Amphiboles, which dominate the Li budget of whole-rocks from the inner part of the complex, have constant delta Li-7 of + 1.8 +/- 2.2 parts per thousand (2 sigma, n = 15). This value reflects a homogeneous melt reservoir and is consistent with their mantle derivation, in agreement with published O and Nd isotopic data. Clinopyroxenes of these samples are consistently lighter, with Delta Li-7(amph-cpx). as large as 8 parts per thousand and are thus not in Li isotope equilibrium. These low values probably reflect late-stage diffusion of Li into clinopyroxene during final cooling of the rocks, thus enriching the clinopyroxene in 6 Li. At the margin of the complex delta(7) Li in the syenites increases systematically, from +2 to high values of + 14 parts per thousand. This, coupled with the observed Li isotope systematics of the granitic country rocks, reflects post-magmatic open-system processes occurring during final cooling of the intrusion. Although the shape and magnitude of the Li isotope and elemental profiles through syenite and country rock are suggestive of diffusion-driven isotope fractionation, they cannot be modeled by one-dimensional diffusive transport and point to circulation of a fluid having a high 67 Li value (possibly seawater) along the chilled contact. In all, this study demonstrates that Li isotopes can be used to identify complex fluid- and diffusion-governed processes taking place during the final cooling of such rocks. (c) 2007 Elsevier B.V All rights reserved.

Conditioning of stochastic 3-D fracture networks to hydrological and geophysical data

The geometry and connectivity of fractures exert a strong influence on the flow and transport properties of fracture networks. We present a novel approach to stochastically generate three-dimensional discrete networks of connected fractures that are conditioned to hydrological and geophysical data. A hierarchical rejection sampling algorithm is used to draw realizations from the posterior probability density function at different conditioning levels. The method is applied to a well-studied granitic formation using data acquired within two boreholes located 6 m apart. The prior models include 27 fractures with their geometry (position and orientation) bounded by information derived from single-hole ground-penetrating radar (GPR) data acquired during saline tracer tests and optical televiewer logs. Eleven cross-hole hydraulic connections between fractures in neighboring boreholes and the order in which the tracer arrives at different fractures are used for conditioning. Furthermore, the networks are conditioned to the observed relative hydraulic importance of the different hydraulic connections by numerically simulating the flow response. Among the conditioning data considered, constraints on the relative flow contributions were the most effective in determining the variability among the network realizations. Nevertheless, we find that the posterior model space is strongly determined by the imposed prior bounds. Strong prior bounds were derived from GPR measurements and helped to make the approach computationally feasible. We analyze a set of 230 posterior realizations that reproduce all data given their uncertainties assuming the same uniform transmissivity in all fractures. The posterior models provide valuable statistics on length scales and density of connected fractures, as well as their connectivity. In an additional analysis, effective transmissivity estimates of the posterior realizations indicate a strong influence of the DFN structure, in that it induces large variations of equivalent transmissivities between realizations. The transmissivity estimates agree well with previous estimates at the site based on pumping, flowmeter and temperature data.

Application of low temperature thermochronology to understanding cooling and exhumation in the Central Swiss Alps

THESIS ABSTRACT : Low-temperature thermochronology relies on application of radioisotopic systems whose closure temperatures are below temperatures at which the dated phases are formed. In that sense, the results are interpreted as "cooling ages" in contrast to "formation ages". Owing to the low closure-temperatures, it is possible to reconstruct exhumation and cooling paths of rocks during their residence at shallow levels of the crust, i.e. within first ~10 km of depth. Processes occurring at these shallow depths such as final exhumation, faulting and relief formation are fundamental for evolution of the mountain belts. This thesis aims at reconstructing the tectono-thermal history of the Aar massif in the Central Swiss Alps by means of zircon (U-Th)/He, apatite (U-Th)/He and apatite fission track thermochronology. The strategy involved acquisition of a large number of samples from a wide range of elevations in the deeply incised Lötschen valley and a nearby NEAT tunnel. This unique location allowed to precisely constrain timing, amount and mechanisms of exhumation of the main orographic feature of the Central Alps, evaluate the role of topography on the thermochronological record and test the impact of hydrothermal activity. Samples were collected from altitudes ranging between 650 and 3930 m and were grouped into five vertical profiles on the surface and one horizontal in the tunnel. Where possible, all three radiometric systems were applied to each sample. Zircon (U-Th)/He ages range from 5.1 to 9.4 Ma and are generally positively correlated with altitude. Age-elevation plots reveal a distinct break in slope, which translates into exhumation rate increasing from ~0.4 to ~3 km/Ma at 6 Ma. This acceleration is independently confirmed by increased cooling rates on the order of 100°C/Ma constrained on the basis of age differences between the zircon (U-Th)/He and the remaining systems. Apatite fission track data also plot on a steep age-elevation curve indicating rapid exhumation until the end of the Miocene. The 6 Ma event is interpreted as reflecting tectonically driven uplift of the Aar massif. The late Miocene timing implies that the increase of precipitation in the Pliocene did not trigger rapid exhumation in the Aar massif. The Messinian salinity crisis in the Mediterranean could not directly intensify erosion of the Aar but associated erosional output from the entire Alps may have tapered the orogenic wedge and caused reactivation of thrusting in the Aar massif. The high exhumation rates in the Messinian were followed by a decrease to ~1.3 km/Ma as evidenced by ~8 km of exhumation during last 6 Ma. The slowing of exhumation is also apparent from apatite (U-Th)1He age-elevation data in the northern part of the Lötschen valley where they plot on a ~0.5km/Ma line and range from 2.4 to 6.4 Ma However, from the apatite (U-Th)/He and fission track data from the NEAT tunnel, there is an indication of a perturbation of the record. The apatite ages are youngest under the axis of the valley, in contrast to an expected pattern where they would be youngest in the deepest sections of the tunnel due to heat advection into ridges. The valley however, developed in relatively soft schists while the ridges are built of solid granitoids. In line with hydrological observations from the tunnel, we suggest that the relatively permeable rocks under the valley floor, served as conduits of geothermal fluids that caused reheating leading to partial Helium loss and fission track annealing in apatites. In consequence, apatite ages from the lowermost samples are too young and the calculated exhumation rates may underestimate true values. This study demonstrated that high-density sampling is indispensable to provide meaningful thermochronological data in the Alpine setting. The multi-system approach allows verifying plausibility of the data and highlighting sources of perturbation. RÉSUMÉ DE THÈSE : La thermochronologie de basse température dépend de l'utilisation de systèmes radiométriques dont la température de fermeture est nettement inférieure à la température de cristallisation du minéral. Les résultats obtenus sont par conséquent interprétés comme des âges de refroidissement qui diffèrent des âges de formation obtenus par le biais d'autres systèmes de datation. Grâce aux températures de refroidissement basses, il est aisé de reconstruire les chemins de refroidissement et d'exhumation des roches lors de leur résidence dans la croute superficielle (jusqu'à 10 km). Les processus qui entrent en jeu à ces faibles profondeurs tels que l'exhumation finale, la fracturation et le faillage ainsi que la formation du relief sont fondamentaux dans l'évolution des chaînes de montagne. Ces dernières années, il est devenu clair que l'enregistrement thermochronologique dans les orogènes peut être influencé par le relief et réinitialisé par l'advection de la chaleur liée à la circulation de fluides géothermaux après le refroidissement initial. L'objectif de cette thèse est de reconstruire l'histoire tectono-thermique du massif de l'Aar dans les Alpes suisses Centrales à l'aide de trois thermochronomètres; (U-Th)/He sur zircon, (U-Th)/He sur apatite et les traces de fission sur apatite. Afin d'atteindre cet objectif, nous avons récolté un grand nombre d'échantillons provenant de différentes altitudes dans la vallée fortement incisée de Lötschental ainsi que du tunnel de NEAT. Cette stratégie d'échantillonnage nous a permis de contraindre de manière précise la chronologie, les quantités et les mécanismes d'exhumation de cette zone des Alpes Centrales, d'évaluer le rôle de la topographie sur l'enregistrement thermochronologique et de tester l'impact de l'hydrothermalisme sur les géochronomètres. Les échantillons ont été prélevés à des altitudes comprises entre 650 et 3930m selon 5 profils verticaux en surface et un dans le tunnel. Quand cela à été possible, les trois systèmes radiométriques ont été appliqués aux échantillons. Les âges (U-Th)\He obtenus sur zircons sont compris entre 5.l et 9.4 Ma et sont corrélés de manière positive avec l'altitude. Les graphiques représentant l'âge et l'élévation montrent une nette rupture de la pente qui traduisent un accroissement de la vitesse d'exhumation de 0.4 à 3 km\Ma il y a 6 Ma. Cette accélération de l'exhumation est confirmée par les vitesses de refroidissement de l'ordre de 100°C\Ma obtenus à partir des différents âges sur zircons et à partir des autres systèmes géochronologiques. Les données obtenues par traces de fission sur apatite nous indiquent également une exhumation rapide jusqu'à la fin du Miocène. Nous interprétons cet évènement à 6 Ma comme étant lié à l'uplift tectonique du massif de l'Aar. Le fait que cet évènement soit tardi-miocène implique qu'une augmentation des précipitations au Pliocène n'a pas engendré cette exhumation rapide du massif de l'Aar. La crise Messinienne de la mer méditerranée n'a pas pu avoir une incidence directe sur l'érosion du massif de l'Aar mais l'érosion associée à ce phénomène à pu réduire le coin orogénique alpin et causer la réactivation des chevauchements du massif de l'Aar. L'exhumation rapide Miocène a été suivie pas une diminution des taux d'exhumation lors des derniers 6 Ma (jusqu'à 1.3 km\Ma). Cependant, les âges (U-Th)\He sur apatite ainsi que les traces de fission sur apatite des échantillons du tunnel enregistrent une perturbation de l'enregistrement décrit ci-dessus. Les âges obtenus sur les apatites sont sensiblement plus jeunes sous l'axe de la vallée en comparaison du profil d'âges attendus. En effet, on attendrait des âges plus jeunes sous les parties les plus profondes du tunnel à cause de l'advection de la chaleur dans les flancs de la vallée. La vallée est creusée dans des schistes alors que les flancs de celle-ci sont constitués de granitoïdes plus durs. En accord avec les observations hydrologiques du tunnel, nous suggérons que la perméabilité élevée des roches sous l'axe de la vallée à permi l'infiltration de fluides géothermaux qui a généré un réchauffement des roches. Ce réchauffement aurait donc induit une perte d'Hélium et un recuit des traces de fission dans les apatites. Ceci résulterait en un rajeunissement des âges apatite et en une sous-estimation des vitesses d'exhumation sous l'axe de la vallée. Cette étude à servi à démontrer la nécessité d'un échantillonnage fin et précis afin d'apporter des données thermochronologiques de qualité dans le contexte alpin. Cette approche multi-système nous a permi de contrôler la pertinence des données acquises ainsi que d'identifier les sources possibles d'erreurs lors d'études thermochronologiques. RÉSUMÉ LARGE PUBLIC Lors d'une orogenèse, les roches subissent un cycle comprenant une subduction, de la déformation, du métamorphisme et, finalement, un retour à la surface (ou exhumation). L'exhumation résulte de la déformation au sein de la zone de collision, menant à un raccourcissement et un apaissessement de l'édifice rocheux, qui se traduit par une remontée des roches, création d'une topographie et érosion. Puisque l'érosion agit comme un racloir sur la partie supérieure de l'édifice, des tentatives de corrélation entre les épisodes d'exhumation rapide et les périodes d'érosion intensive, dues aux changements climatiques, ont été effectuées. La connaissance de la chronologie et du lieu précis est d'une importance capitale pour une quelconque reconstruction de l'évolution d'une chaîne de montagne. Ces critères sont donnés par un retraçage des changements de la température de la roche en fonction du temps, nous donnant le taux de refroidissement. L'instant auquel les roches ont refroidit, passant une certaine température, est contraint par l'application de techniques de datation par radiométrie. Ces méthodes reposent sur la désintégration des isotopes radiogéniques, tels que l'uranium et le potassium, tous deux abondants dans les roches de la croûte terrestre. Les produits de cette désintégration ne sont pas retenus dans les minéraux hôtes jusqu'au moment du refroidissement de la roche sous une température appelée 'de fermeture' , spécifique à chaque système de datation. Par exemple, la désintégration radioactive des atomes d'uranium et de thorium produit des atomes d'hélium qui s'échappent d'un cristal de zircon à des températures supérieures à 200°C. En mesurant la teneur en uranium-parent, l'hélium accumulé et en connaissant le taux de désintégration, il est possible de calculer à quel moment la roche échantillonnée est passée sous la température de 200°C. Si le gradient géothermal est connu, les températures de fermeture peuvent être converties en profondeurs actuelles (p. ex. 200°C ≈ 7km), et le taux de refroidissement en taux d'exhumation. De plus, en datant par système radiométrique des échantillons espacés verticalement, il est possible de contraindre directement le taux d'exhumation de la section échantillonnée en observant les différences d'âges entre des échantillons voisins. Dans les Alpes suisses, le massif de l'Aar forme une structure orographique majeure. Avec des altitudes supérieures à 4000m et un relief spectaculaire de plus de 2000m, le massif domine la partie centrale de la chaîne de montagne. Les roches aujourd'hui exposées à la surface ont été enfouies à plus de 10 km de profond il y a 20 Ma, mais la topographie actuelle du massif de l'Aar semble surtout s'être développée par un soulèvement actif depuis quelques millions d'années, c'est-à-dire depuis le Néogène supérieur. Cette période comprend un changement climatique soudain ayant touché l'Europe il y a environ 5 Ma et qui a occasionné de fortes précipitations, entraînant certainement une augmentation de l'érosion et accélérant l'exhumation des Alpes. Dans cette étude, nous avons employé le système de datation (U-TH)/He sur zircon, dont la température de fermeture de 200°C est suffisamment basse pour caractériser l'exhumation du Néogène sup. /Pliocène. Les échantillons proviennent du Lötschental et du tunnel ferroviaire le plus profond du monde (NEAT) situé dans la partie ouest du massif de l'Aar. Considérés dans l'ensemble, ces échantillons se répartissent sur un dénivelé de 3000m et des âges de 5.1 à 9.4 Ma. Les échantillons d'altitude supérieure (et donc plus vieux) documentent un taux d'exhumation de 0.4 km/Ma jusqu'à il y a 6 Ma, alors que les échantillons situés les plus bas ont des âges similaires allant de 6 à 5.4 Ma, donnant un taux jusqu'à 3km /Ma. Ces données montrent une accélération dramatique de l'exhumation du massif de l'Aar il y a 6 Ma. L'exhumation miocène sup. du massif prédate donc le changement climatique Pliocène. Cependant, lors de la crise de salinité d'il y a 6-5.3 Ma (Messinien), le niveau de la mer Méditerranée est descendu de 3km. Un tel abaissement de la surface d'érosion peut avoir accéléré l'exhumation des Alpes, mais le bassin sud alpin était trop loin du massif de l'Aar pour influencer son érosion. Nous arrivons à la conclusion que la datation (U-Th)/He permet de contraindre précisément la chronologie et l'exhumation du massif de l'Aar. Concernant la dualité tectonique-érosion, nous suggérons que, dans le cas du massif de l'Aar, la tectonique prédomine.

Stochastic stability and the evolution of coordination in spatially structured populations.

Animals can often coordinate their actions to achieve mutually beneficial outcomes. However, this can result in a social dilemma when uncertainty about the behavior of partners creates multiple fitness peaks. Strategies that minimize risk ("risk dominant") instead of maximizing reward ("payoff dominant") are favored in economic models when individuals learn behaviors that increase their payoffs. Specifically, such strategies are shown to be "stochastically stable" (a refinement of evolutionary stability). Here, we extend the notion of stochastic stability to biological models of continuous phenotypes at a mutation-selection-drift balance. This allows us to make a unique prediction for long-term evolution in games with multiple equilibria. We show how genetic relatedness due to limited dispersal and scaled to account for local competition can crucially affect the stochastically-stable outcome of coordination games. We find that positive relatedness (weak local competition) increases the chance the payoff dominant strategy is stochastically stable, even when it is not risk dominant. Conversely, negative relatedness (strong local competition) increases the chance that strategies evolve that are neither payoff nor risk dominant. Extending our results to large multiplayer coordination games we find that negative relatedness can create competition so extreme that the game effectively changes to a hawk-dove game and a stochastically stable polymorphism between the alternative strategies evolves. These results demonstrate the usefulness of stochastic stability in characterizing long-term evolution of continuous phenotypes: the outcomes of multiplayer games can be reduced to the generic equilibria of two-player games and the effect of spatial structure can be analyzed readily.

Is it worth treating fever in intensive care unit patients? Preliminary results from a randomized trial of the effect of external cooling.

BACKGROUND: Antipyresis is a common clinical practice in intensive care, although it is unknown if fever is harmful, beneficial, or a negligible adverse effect of infection and inflammation. METHODS: In a randomized study, rectal temperature and discomfort were assessed in 38 surgical intensive care unit patients without neurotrauma or severe hypoxemia and with fever (temperature >/=38.5 degrees C) and systemic inflammatory response syndrome. Eighteen patients received external cooling while 20 received no antipyretic treatment. RESULTS: Temperature and discomfort decreased similarly in both groups after 24 hours. No significant differences in recurrence of fever, incidence of infection, antibiotic therapy, intensive care unit and hospital length of stay, or mortality were noted between the groups. CONCLUSIONS: These results suggest that the systematic suppression of fever may not be useful in patients without severe cranial trauma or significant hypoxemia. Letting fever take its natural course does not seem to harm patients with systemic inflammatory response syndrome or influence the discomfort level and may save costs.

Rates of cultural change and patterns of cultural accumulation in stochastic models of social transmission.

Cultural variation in a population is affected by the rate of occurrence of cultural innovations, whether such innovations are preferred or eschewed, how they are transmitted between individuals in the population, and the size of the population. An innovation, such as a modification in an attribute of a handaxe, may be lost or may become a property of all handaxes, which we call "fixation of the innovation." Alternatively, several innovations may attain appreciable frequencies, in which case properties of the frequency distribution-for example, of handaxe measurements-is important. Here we apply the Moran model from the stochastic theory of population genetics to study the evolution of cultural innovations. We obtain the probability that an initially rare innovation becomes fixed, and the expected time this takes. When variation in cultural traits is due to recurrent innovation, copy error, and sampling from generation to generation, we describe properties of this variation, such as the level of heterogeneity expected in the population. For all of these, we determine the effect of the mode of social transmission: conformist, where there is a tendency for each naïve newborn to copy the most popular variant; pro-novelty bias, where the newborn prefers a specific variant if it exists among those it samples; one-to-many transmission, where the variant one individual carries is copied by all newborns while that individual remains alive. We compare our findings with those predicted by prevailing theories for rates of cultural change and the distribution of cultural variation.

Stochastic Population Projection for Germany - based on the Quadratic Spline approach to modelling age specific fertility rates

This contribution builds upon a former paper by the authors (Lipps and Betz 2004), in which a stochastic population projection for East- and West Germany is performed. Aim was to forecast relevant population parameters and their distribution in a consistent way. We now present some modifications, which have been modelled since. First, population parameters for the entire German population are modelled. In order to overcome the modelling problem of the structural break in the East during reunification, we show that the adaptation process of the relevant figures by the East can be considered to be completed by now. As a consequence, German parameters can be modelled just by using the West German historic patterns, with the start-off population of entire Germany. Second, a new model to simulate age specific fertility rates is presented, based on a quadratic spline approach. This offers a higher flexibility to model various age specific fertility curves. The simulation results are compared with the scenario based official forecasts for Germany in 2050. Exemplary for some population parameters (e.g. dependency ratio), it can be shown that the range spanned by the medium and extreme variants correspond to the s-intervals in the stochastic framework. It seems therefore more appropriate to treat this range as a s-interval covering about two thirds of the true distribution.

On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

Essays on the treatment of cash flows under stochastic interest rates

Abstract This paper shows how to calculate recursively the moments of the accumulated and discounted value of cash flows when the instantaneous rates of return follow a conditional ARMA process with normally distributed innovations. We investigate various moment based approaches to approximate the distribution of the accumulated value of cash flows and we assess their performance through stochastic Monte-Carlo simulations. We discuss the potential use in insurance and especially in the context of Asset-Liability Management of pension funds.