Explicit ruin formulas for models with dependence among risks

We show that a simple mixing idea allows one to establish a number of explicit formulas for ruin probabilities and related quantities in collective risk models with dependence among claim sizes and among claim inter-occurrence times. Examples include compound Poisson risk models with completely monotone marginal claim size distributions that are dependent according to Archimedean survival copulas as well as renewal risk models with dependent inter-occurrence times.

Ruin Theory with Excess of Loss Reinsurance and Reinstatements

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. (C) 2011 Elsevier Inc. All rights reserved.

Properties of a risk measure derived from ruin theory

This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level. This VaR-type risk measure turns out to be equivalent to the VaR of the maximal deficit of the ruin process in infinite time. A related Tail-VaR-type risk measure is also discussed.

Ruin and related quantities in some advanced insurance risk models

Risk theory has been a very active research area over the last decades. The main objectives of the theory are to find adequate stochastic processes which can model the surplus of a (non-life) insurance company and to analyze the risk related quantities such as ruin time, ruin probability, expected discounted penalty function and expected discounted dividend/tax payments. The study of these ruin related quantities provides crucial information for actuaries and decision makers. This thesis consists of the study of four different insurance risk models which are essentially related. The ruin and related quantities are investigated by using different techniques, resulting in explicit or asymptotic expressions for the ruin time, the ruin probability, the expected discounted penalty function and the expected discounted tax payments. - La recherche en théorie du risque a été très dynamique au cours des dernières décennies. D'un point de vue théorique, les principaux objectifs sont de trouver des processus stochastiques adéquats permettant de modéliser le surplus d'une compagnie d'assurance non vie et d'analyser les mesures de risque, notamment le temps de ruine, la probabilité de ruine, l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes. L'étude de ces mesures associées à la ruine fournit des informations cruciales pour les actuaires et les décideurs. Cette thèse consiste en l'étude des quatre différents modèles de risque d'assurance qui sont essentiellement liés. La ruine et les mesures qui y sont associées sont examinées à l'aide de différentes techniques, ce qui permet d'induire des expressions explicites ou asymptotiques du temps de ruine, de la probabilité de ruine, de l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes.

Ruin problems under IBNR Dynamics

In this paper, we consider a discrete-time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg-type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non-delayed risk model, and numerical simulations are carried out with Belgian market data.

A risk model with an observer in a Markov environment

We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.

Progesterone down-regulates the open probability of the amiloride-sensitive epithelial sodium channel via a Nedd4-2-dependent mechanism.

Activation of the mitogen-activated protein (MAP) kinase cascade by progesterone in Xenopus oocytes leads to a marked down-regulation of activity of the amiloride-sensitive epithelial sodium channel (ENaC). Here we have studied the signaling pathways involved in progesterone effect on ENaC activity. We demonstrate that: (i) the truncation of the C termini of the alphabetagammaENaC subunits results in the loss of the progesterone effect on ENaC; (ii) the effect of progesterone was also suppressed by mutating conserved tyrosine residues in the Pro-X-X-Tyr (PY) motif of the C termini of the beta and gamma ENaC subunits (beta(Y618A) and gamma(Y628A)); (iii) the down-regulation of ENaC activity by progesterone was also suppressed by co-expression ENaC subunits with a catalytically inactive mutant of Nedd4-2, a ubiquitin ligase that has been previously demonstrated to decrease ENaC cell-surface expression via a ubiquitin-dependent internalization/degradation mechanism; (iv) the effect of progesterone was significantly reduced by suppression of consensus sites (beta(T613A) and gamma(T623A)) for ENaC phosphorylation by the extracellular-regulated kinase (ERK), a MAP kinase previously shown to facilitate the binding of Nedd4 ubiquitin ligases to ENaC; (v) the quantification of cell-surface-expressed ENaC subunits revealed that progesterone decreases ENaC open probability (whole cell P(o), wcP(o)) and not its cell-surface expression. Collectively, these results demonstrate that the binding of active Nedd4-2 to ENaC is a crucial step in the mechanism of ENaC inhibition by progesterone. Upon activation of ERK, the effect of Nedd4-2 on ENaC open probability can become more important than its effect on ENaC cell-surface expression.

Probability of achieving optimal molecular response to imatinib in chronic myeloid leukemia (CML) patients: Pharmacokinetic/Pharmacodynamic (PK/PD) relationships observed under field-conditions

Objectives: Imatinib has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations (Cmin) correlate with response rates in CML patients. This analysis aimed to evaluate the impact of imatinib exposure on optimal molecular response rates in a large European cohort of patients followed by centralized TDM.¦Methods: Sequential PK/PD analysis was performed in NONMEM 7 on 2230 plasma (PK) samples obtained along with molecular response (PD) data from 1299 CML patients. Model-based individual Bayesian estimates of exposure, parameterized as to initial dose adjusted and log-normalized Cmin (log-Cmin) or clearance (CL), were investigated as potential predictors of optimal molecular response, while accounting for time under treatment (stratified at 3 years), gender, CML phase, age, potentially interacting comedication, and TDM frequency. PK/PD analysis used mixed-effect logistic regression (iterative two-stage method) to account for intra-patient correlation.¦Results: In univariate analyses, CL, log-Cmin, time under treatment, TDM frequency, gender (all p<0.01) and CML phase (p=0.02) were significant predictors of the outcome. In multivariate analyses, all but log-Cmin remained significant (p<0.05). Our model estimates a 54.1% probability of optimal molecular response in a female patient with a median CL of 14.4 L/h, increasing by 4.7% with a 35% decrease in CL (percentile 10 of CL distribution), and decreasing by 6% with a 45% increased CL (percentile 90), respectively. Male patients were less likely than female to be in optimal response (odds ratio: 0.62, p<0.001), with an estimated probability of 42.3%.¦Conclusions: Beyond CML phase and time on treatment, expectedly correlated to the outcome, an effect of initial imatinib exposure on the probability of achieving optimal molecular response was confirmed in field-conditions by this multivariate analysis. Interestingly, male patients had a higher risk of suboptimal response, which might not exclusively derive from their 18.5% higher CL, but also from reported lower adherence to the treatment. A prospective longitudinal study would be desirable to confirm the clinical importance of identified covariates and to exclude biases possibly affecting this observational survey.

Activity in inferior parietal and medial prefrontal cortex signals the accumulation of evidence in a probability learning task.

In an uncertain environment, probabilities are key to predicting future events and making adaptive choices. However, little is known about how humans learn such probabilities and where and how they are encoded in the brain, especially when they concern more than two outcomes. During functional magnetic resonance imaging (fMRI), young adults learned the probabilities of uncertain stimuli through repetitive sampling. Stimuli represented payoffs and participants had to predict their occurrence to maximize their earnings. Choices indicated loss and risk aversion but unbiased estimation of probabilities. BOLD response in medial prefrontal cortex and angular gyri increased linearly with the probability of the currently observed stimulus, untainted by its value. Connectivity analyses during rest and task revealed that these regions belonged to the default mode network. The activation of past outcomes in memory is evoked as a possible mechanism to explain the engagement of the default mode network in probability learning. A BOLD response relating to value was detected only at decision time, mainly in striatum. It is concluded that activity in inferior parietal and medial prefrontal cortex reflects the amount of evidence accumulated in favor of competing and uncertain outcomes.

Lumbar spine texture enhances 10-year fracture probability assessment.

We found that lumbar spine texture analysis using trabecular bone score (TBS) is a risk factor for MOF and a risk factor for death in a retrospective cohort study from a large clinical registry for the province of Manitoba, Canada. INTRODUCTION: FRAX® estimates the 10-year probability of major osteoporotic fracture (MOF) using clinical risk factors and femoral neck bone mineral density (BMD). Trabecular bone score (TBS), derived from texture in the spine dual X-ray absorptiometry (DXA) image, is related to bone microarchitecture and fracture risk independently of BMD. Our objective was to determine whether TBS provides information on MOF probability beyond that provided by the FRAX variables. METHODS: We included 33,352 women aged 40-100 years (mean 63 years) with baseline DXA measurements of lumbar spine TBS and femoral neck BMD. The association between TBS, the FRAX variables, and the risk of MOF or death was examined using an extension of the Poisson regression model. RESULTS: During the mean of 4.7 years, 1,754 women died and 1,872 sustained one or more MOF. For each standard deviation reduction in TBS, there was a 36 % increase in MOF risk (HR 1.36, 95 % CI 1.30-1.42, p < 0.001) and a 32 % increase in death (HR 1.32, 95 % CI 1.26-1.39, p < 0.001). When adjusted for significant clinical risk factors and femoral neck BMD, lumbar spine TBS was still a significant predictor of MOF (HR 1.18, 95 % CI 1.12-1.23) and death (HR 1.20, 95 % CI 1.14-1.26). Models for estimating MOF probability, accounting for competing mortality, showed that low TBS (10th percentile) increased risk by 1.5-1.6-fold compared with high TBS (90th percentile) across a broad range of ages and femoral neck T-scores. CONCLUSIONS: Lumbar spine TBS is able to predict incident MOF independent of FRAX clinical risk factors and femoral neck BMD even after accounting for the increased death hazard.