Moments of the Discounted Aggregate Claims with Delay Inter-Occurrence Distribution and Dependence Introduced by a FGM Copula

In this chapter, with renewal argument, we derive higher simple moments of the Discounted Compound Delay Renewal Risk Process (DCDRRP) when introducing dependence between the inter-occurrence time and the subsequent claim size. To illustrate our results, we assume that the inter-occurrence time is following a delay-Poisson process and the claim amounts is following a mixture of Exponential distribution, we then provide numerical results for the first two moments. The dependence structure between the inter-occurrence time and the subsequent claim size is defined by a Farlie-Gumbel-Morgenstern copula. Assuming that the claim distribution has finite moments, we obtain a general formula for all the moments of the DCDRRP process

Distribution of multi-states models in health insurance under semi-Markovian assumptions

Abstract:In this paper we develop a system of integral and differential equations forth estate wise probability distributions of the present value of future payments on a multi-states life insurance policy under semi-Markov assumptions. We also provide formulas on the probability distribution through inversion techniques on the respective moment generating functions of the present value of future payments. The results are illustrated with applications to Value-at-Risk (VaR) and TailValue-at-Risk (TVaR) calculations

Asymptotic tail probability for the discounted aggregate sums in a time dependent renewal risk model

This paper presents an extension of the classical compound Poisson risk model in which the inter-claim time arrivals and the claim amounts are structurally dependent. We derive the corresponding asymptotic tail probabilities for the discounted aggregate claims in a finite insurance contract under constant force of interest. The dependence assumption between the inter-claim times and the claim amounts is well suited for insurance contracts during extreme and catastrophic events. Based on the existing literature, we use heavytailed distributions for the discounted aggregate claims and derive the extreme value at risk (minimum capital requirement). Our results, based on a case study of ten million simulations, show that the independence assumption between the inter-claim times and the claim amounts lead to underestimating the minimum capital requirement proposed by the regulatory authorities

Moments of Phase-type aging modeling for health dependent costs

Abstract: In this paper, we use a discrete time Phase-type process to model the health care cost of an insurance contract by considering all possible critical health states of an individual with constant interest rate. From the moment generating function of the NPV, we derive a recursive formula of this Markov Reward Model (MRM)

Mycobacterium bolletii Respiratory Infections

Contrary to other species in the Mycobacterium chelonae-abscessus complex, we reidentified M. bolletii strains isolated from 4 respiratory patients and found these strains to be uniformly resistant to clarithromycin. No mutations previously associated with macrolide resistance in bacteria were detected in either the 23S rDNA or the genes encoding riboproteins L4 and L22

Asymptotic tail probability of the discounted aggregate claims under homogeneous, non-homogeneous and mixed poisson risk model

Abstract: In this paper, we derive a closed-form expression of the tail probability of the aggregate discounted claims under homogeneous, non-homogeneous and mixed Poisson risk models with constant force of interest by using a general dependence structure between the inter-occurrence time and the claim sizes. This dependence structure is relevant since it is well known that under catastrophic or extreme events the inter-occurrence time and the claim severities are dependent

Core Gene Set As the Basis of Multilocus Sequence Analysis of the Subclass Actinobacteridae

Comparative genomic sequencing is shedding new light on bacterial identification, taxonomy and phylogeny. An in silico assessment of a core gene set necessary for cellular functioning was made to determine a consensus set of genes that would be useful for the identification, taxonomy and phylogeny of the species belonging to the subclass Actinobacteridae which contained two orders Actinomycetales and Bifidobacteriales. The subclass Actinobacteridae comprised about 85% of the actinobacteria families. The following recommended criteria were used to establish a comprehensive gene set; the gene should (i) be long enough to contain phylogenetically useful information, (ii) not be subject to horizontal gene transfer, (iii) be a single copy (iv) have at least two regions sufficiently conserved that allow the design of amplification and sequencing primers and (v) predict whole-genome relationships. We applied these constraints to 50 different Actinobacteridae genomes and made 1,224 pairwise comparisons of the genome conserved regions and gene fragments obtained by using Sequence VARiability Analysis Program (SVARAP), which allow designing the primers. Following a comparative statistical modeling phase, 3 gene fragments were selected, ychF, rpoB, and secY with R2>0.85. Selected sets of broad range primers were tested from the 3 gene fragments and were demonstrated to be useful for amplification and sequencing of 25 species belonging to 9 genera of Actinobacteridae. The intraspecies similarities were 96.3–100% for ychF, 97.8–100% for rpoB and 96.9–100% for secY among 73 strains belonging to 15 species of the subclass Actinobacteridae compare to 99.4–100% for 16S rRNA. The phylogenetic topology obtained from the combined datasets ychF+rpoB+secY was globally similar to that inferred from the 16S rRNA but with higher confidence. It was concluded that multi-locus sequence analysis using core gene set might represent the first consensus and valid approach for investigating the bacterial identification, phylogeny and taxonomy