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.

The contributions of sensory dominance and attentional bias to cross-modal enhancement of visual cortex excitability.

Approaching or looming sounds (L-sounds) have been shown to selectively increase visual cortex excitability [Romei, V., Murray, M. M., Cappe, C., & Thut, G. Preperceptual and stimulus-selective enhancement of low-level human visual cortex excitability by sounds. Current Biology, 19, 1799-1805, 2009]. These cross-modal effects start at an early, preperceptual stage of sound processing and persist with increasing sound duration. Here, we identified individual factors contributing to cross-modal effects on visual cortex excitability and studied the persistence of effects after sound offset. To this end, we probed the impact of different L-sound velocities on phosphene perception postsound as a function of individual auditory versus visual preference/dominance using single-pulse TMS over the occipital pole. We found that the boosting of phosphene perception by L-sounds continued for several tens of milliseconds after the end of the L-sound and was temporally sensitive to different L-sound profiles (velocities). In addition, we found that this depended on an individual's preferred sensory modality (auditory vs. visual) as determined through a divided attention task (attentional preference), but not on their simple threshold detection level per sensory modality. Whereas individuals with "visual preference" showed enhanced phosphene perception irrespective of L-sound velocity, those with "auditory preference" showed differential peaks in phosphene perception whose delays after sound-offset followed the different L-sound velocity profiles. These novel findings suggest that looming signals modulate visual cortex excitability beyond sound duration possibly to support prompt identification and reaction to potentially dangerous approaching objects. The observed interindividual differences favor the idea that unlike early effects this late L-sound impact on visual cortex excitability is influenced by cross-modal attentional mechanisms rather than low-level sensory processes.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

An allele-specific, stochastic gene expression process controls the expression of multiple Ly49 family genes and generates a diverse, MHC-specific NK cell receptor repertoire.

Mouse NK cells express MHC class I-specific inhibitory Ly49 receptors. Since these receptors display distinct ligand specificities and are clonally distributed, their expression generates a diverse NK cell receptor repertoire specific for MHC class I molecules. We have previously found that the Dd (or Dk)-specific Ly49A receptor is usually expressed from a single allele. However, a small fraction of short-term NK cell clones expressed both Ly49A alleles, suggesting that the two Ly49A alleles are independently and randomly expressed. Here we show that the genes for two additional Ly49 receptors (Ly49C and Ly49G2) are also expressed in a (predominantly) mono-allelic fashion. Since single NK cells can co-express multiple Ly49 receptors, we also investigated whether mono-allelic expression from within the tightly linked Ly49 gene cluster is coordinate or independent. Our clonal analysis suggests that the expression of alleles of distinct Ly49 genes is not coordinate. Thus Ly49 alleles are apparently independently and randomly chosen for stable expression, a process that directly restricts the number of Ly49 receptors expressed per single NK cell. We propose that the Ly49 receptor repertoire specific for MHC class I is generated by an allele-specific, stochastic gene expression process that acts on the entire Ly49 gene cluster.

Initiation and limitation of Ly-49A NK cell receptor acquisition by T cell factor-1.

The establishment of clonally variable expression of MHC class I-specific receptors by NK cells is not well understood. The Ly-49A receptor is used by approximately 20% of NK cells, whereby most cells express either the maternal or paternal allele and few express simultaneously both alleles. We have previously shown that NK cells expressing Ly-49A were reduced or almost absent in mice harboring a single or no functional allele of the transcription factor T cell factor-1 (TCF-1), respectively. In this study, we show that enforced expression of TCF-1 in transgenic mice yields an expanded Ly-49A subset. Even though the frequencies of Ly-49A(+) NK cells varied as a function of the TCF-1 dosage, the relative abundance of mono- and biallelic Ly-49A cells was maintained. Mono- and biallelic Ly-49A NK cells were also observed in mice expressing exclusively a transgenic TCF-1, i.e., expressing a fixed amount of TCF-1 in all NK cells. These findings suggest that Ly-49A acquisition is a stochastic event due to limiting TCF-1 availability, rather than the consequence of clonally variable expression of the endogenous TCF-1 locus. Efficient Ly-49A acquisition depended on the expression of a TCF-1 isoform, which included a domain known to associate with the TCF-1 coactivator beta-catenin. Indeed, the proximal Ly-49A promoter was beta-catenin responsive in reporter gene assays. We thus propose that Ly-49A receptor expression is induced from a single allele in occasional NK cells due to a limitation in the amount of a transcription factor complex requiring TCF-1.

Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities.

Quantifying the spatial configuration of hydraulic conductivity (K) in heterogeneous geological environments is essential for accurate predictions of contaminant transport, but is difficult because of the inherent limitations in resolution and coverage associated with traditional hydrological measurements. To address this issue, we consider crosshole and surface-based electrical resistivity geophysical measurements, collected in time during a saline tracer experiment. We use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology to jointly invert the dynamic resistivity data, together with borehole tracer concentration data, to generate multiple posterior realizations of K that are consistent with all available information. We do this within a coupled inversion framework, whereby the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration. To minimize computational expense, a facies-based subsurface parameterization is developed. The Bayesian-McMC methodology allows us to explore the potential benefits of including the geophysical data into the inverse problem by examining their effect on our ability to identify fast flowpaths in the subsurface, and their impact on hydrological prediction uncertainty. Using a complex, geostatistically generated, two-dimensional numerical example representative of a fluvial environment, we demonstrate that flow model calibration is improved and prediction error is decreased when the electrical resistivity data are included. The worth of the geophysical data is found to be greatest for long spatial correlation lengths of subsurface heterogeneity with respect to wellbore separation, where flow and transport are largely controlled by highly connected flowpaths.

Reduced left hemisphere dominance for multiple versus single anagram solutions and its modulation by individuals' schizotypy

Problem solving (including insight, divergent thinking) seems to rely on the right hemisphere (RH). These functions are difficult to assess behaviorally. We propose anagram resolution as a suitable paradigm. University students (n=32) performed three tachistoscopic lateralized visual half-field experiments (stimulus presentation 150ms). In Experiment 1, participants recalled four-letter strings. Subsequently, participants provided solutions for four-letter anagrams (one solution in Experiment 2; two solutions in Experiment 3). Additionally, participants completed a schizotypy questionnaire (O-LIFE). Results showed a right visual field advantage in Experiment 1 and 2, but no visual field advantage in Experiment 3. In Experiment 1, increasing positive schizotypy associated with a RH performance shift. Problem solving seems to require increasingly the RH when facing several rather than one solution. This result supports previous studies on the RH's role in remote associative, metaphor and discourse processing. The more complex language requirements, the less personality traits seem to matter.

How Social Dominance Orientation affects union participation: The role of union identification and perceived union instrumentality

Bridging social dominance theory and labour studies, this field study investigated the mechanisms underpinning the relationship between rejection of group-based domination and participation in union activities. Respondents (N = 135) were members of a public sector union in California, that is, a hierarchy-attenuating institution. Results revealed that union identification mediated the negative relationship between social dominance orientation and active union participation. Moreover, the mediational effect of union identification was moderated by perceived union instrumentality (i.e. outcome- and process-based benefits afforded by the union), indicating that the relationship between union identification and participation was stronger among those union members who consider that the union affects workplace justice. The findings reveal the importance of both identity-based and instrumental motivations underlying union participation. The novelty of applying social dominance theory to union behaviour is underscored.

Discovery-dominance trade-off among widespread invasive ant species

Ants are among the most problematic invasive species. They displace numerous native species, alter ecosystem processes, and can have negative impacts on agriculture and human health. In part, their success might stem from a departure from the discovery-dominance trade-off that can promote co-existence in native ant communities, that is, invasive ants are thought to be at the same time behaviorally dominant and faster discoverers of resources, compared to native species. However, it has not yet been tested whether similar asymmetries in behavioral dominance, exploration, and recruitment abilities also exist among invasive species. Here, we establish a dominance hierarchy among four of the most problematic invasive ants (Linepithema humile, Lasius neglectus, Wasmannia auropunctata, Pheidole megacephala) that may be able to arrive and establish in the same areas in the future. To assess behavioral dominance, we used confrontation experiments, testing the aggressiveness in individual and group interactions between all species pairs. In addition, to compare discovery efficiency, we tested the species' capacity to locate a food resource in a maze, and the capacity to recruit nestmates to exploit a food resource. The four species differed greatly in their capacity to discover resources and to recruit nestmates and to dominate the other species. Our results are consistent with a discovery-dominance trade-off. The species that showed the highest level of interspecific aggressiveness and dominance during dyadic interactions.