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We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to $n$ insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the…

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…

Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…

Pricing decisions of companies require an understanding of the causal effect of a price change on the demand. When real-life pricing experiments are infeasible, data-driven decision-making must be based on alternative data sources such as…

Heavy-tailed random variables have been used in insurance research to model both loss frequencies and loss severities, with substantially more emphasis on the latter. In the present work, we take a step toward addressing this imbalance by…

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…

The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of…

An insurance company is required to prepare a certain amount of money, called reserve, as a mean to pay its policy holders claims in the future. There are several types of reserve, one of them is IBNR reserve, for which the payments are…

Contemporary insurance theory is concentrated on models with different types of polices and shock events may influence the payments on some of them. Jordanova (2018) considered a model where a shock event contributes to the total claim…

Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of…

The estimation of asset return distributions is crucial for determining optimal trading strategies. In this paper we describe the constrained mixture model, based on a mixture of Gamma and Gaussian distributions, to provide an accurate…

Prediction modelling of claim frequency is an important task for pricing and risk management in non-life insurance and needed to be updated frequently with the changes in the insured population, regulatory legislation and technology.…

The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the…

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…

In this paper, non-life insurance claims were modelled under the three parameter discrete generalised Pareto distribution. Data from the National Insurance Commission of Ghana on reported and settled claims were considered for the period…

In the current insurance literature, prediction of insurance claims in the regression problem is often performed with a statistical model. This model-based approach may potentially suffer from several drawbacks: (i) model misspecification,…

Classical Bayesian mechanism design relies on the common prior assumption, but such prior is often not available in practice. We study the design of prior-independent mechanisms that relax this assumption: the seller is selling an…

We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…

We propose a prior distribution for the number of components of a finite mixture model. The novelty is that the prior distribution is obtained by considering the loss one would incur if the true value representing the number of components…