Bonus-malus Systems in a Deregulated Environment: Forecasting Market Shares Using Diffusion Models

In a deregulated insurance market, insurance carriers have an incentive to be innovative in their pricing decisions by segmenting their portfolios and designing new bonus-malus systems (BMS). This paper examines the evolution of market shares and claim frequencies in a two-company market, when one insurer breaks off the existing stability by introducing a super-discount class in its BMS. Several assumptions concerning policyholders and insurers behavior are tested. Diffusion theory is used to model the spread of the information concerning the new BMS among prospective customers. A wide variety of market outcomes results: one company may take over the market or the two may survive with equal or unequal market shares, each specializing in a specific niche of the market. Before engaging in an aggressive competitive behavior, insurers should consequently be reasonably confident in their assumptions concerning the reactions of their policyholders to the new BMS

A “square-root rule” for reinsurance? Evidence from several national markets

Purpose – Using a game-theoretic model of insurance markets, Powers and Shubik in 2001 derived a mathematical expression for the optimal number of reinsurers for a given number of primary insurers. Subsequently in 2005, Powers and Shubik showed analytically that, for large numbers of primary insurers, this expression is effectively a “square-root rule”, i.e. the optimal number of reinsurers in a market is given asymptotically by the square root of the total number of primary insurers. In this paper, we test the accuracy of the square-root rule empirically. Design/methodology/approach – The numbers of primary insurers and reinsurers existing in a range of 18-20 different national insurance markets over a period of 11 years are used. Findings – The empirical results are consistent with the square-root rule. In addition, we find that the number of reinsurers may also be associated with the market's willingness to pay for risk. When the market's perception of risk is high, there is a greater supply of reinsurance to provide capacity to primary insurers. Originality/value – An empirical model is presented that deals explicitly with the number of insurers and reinsurers in a market. This is of value to government policymakers and insurance regulators.Game theory, Insurance, Reinsurance

Comparative performances of machine learning methods for classifying Crohn Disease patients using genome-wide genotyping data

Abstract: Crohn Disease (CD) is a complex genetic disorder for which more than 140 genes have been identified using genome wide association studies (GWAS). However, the genetic architecture of the trait remains largely unknown. The recent development of machine learning (ML) approaches incited us to apply them to classify healthy and diseased people according to their genomic information. The Immunochip dataset containing 18,227 CD patients and 34,050 healthy controls enrolled and genotyped by the international Inflammatory Bowel Disease genetic consortium (IIBDGC) has been re-analyzed using a set of ML methods: penalized logistic regression (LR), gradient boosted trees (GBT) and artificial neural networks (NN). The main score used to compare the methods was the Area Under the ROC Curve (AUC) statistics. The impact of quality control (QC), imputing and coding methods on LR results showed that QC methods and imputation of missing genotypes may artificially increase the scores. At the opposite, neither the patient/control ratio nor marker preselection or coding strategies significantly affected the results. LR methods, including Lasso, Ridge and ElasticNet provided similar results with a maximum AUC of 0.80. GBT methods like XGBoost, LightGBM and CatBoost, together with dense NN with one or more hidden layers, provided similar AUC values, suggesting limited epistatic effects in the genetic architecture of the trait. ML methods detected near all the genetic variants previously identified by GWAS among the best predictors plus additional predictors with lower effects. The robustness and complementarity of the different methods are also studied. Compared to LR, non-linear models such as GBT or NN may provide robust complementary approaches to identify and classify genetic markers

Ultra high-resolution fMRI and electrophysiology of the rat primary somatosensory cortex

High-resolution functional-magnetic-resonance-imaging (fMRI) has been used to study brain functions at increasingly finer scale, but whether fMRI can accurately reflect layer-specific neuronal activities is less well understood. The present study investigated layer-specific cerebral-blood-volume (CBV) fMRI and electrophysiological responses in the rat cortex. CBV fMRI at 40×40 µm in-plane resolution was performed on an 11.7-T scanner. Electrophysiology used a 32-channel electrode array that spanned the entire cortical depth. Graded electrical stimulation was used to study activations in different cortical layers, exploiting the notion that most of the sensory-specific neurons are in layers II–V and most of the nociceptive-specific neurons are in layers V–VI. CBV response was strongest in layer IV of all stimulus amplitudes. Current source density analysis showed strong sink currents at cortical layers IV and VI. Multi-unit activities mainly appeared at layers IV–VI and peaked at layer V. Although our measures showed scaled activation profiles during modulation of stimulus amplitude and failed to detect specific recruitment at layers V and VI during noxious electrical stimuli, there appears to be discordance between CBV fMRI and electrophysiological peak responses, suggesting neurovascular uncoupling at laminar resolution. The technique implemented in the present study offers a means to investigate intracortical neurovascular function in the normal and diseased animal models at laminar resolution