This study introduces a new family of distributions (FoD) called type I heavy-tailed odd Burr III-G (TI-HT-OBIII-G) distribution. Several statistical properties of the family are derived along with actuarial risk measures. The maximum likelihood estimation (MLE) approach is adopted in the...

Longevity risk affecting older adults can be transferred to the insurance market by purchasing a lifetime annuity. Special-rate life annuities, which are priced, among other factors, on the basis of health and lifestyle factors, go beyond traditional considerations of age and sex by using...

This paper aims to develop optional semimartingale methods in risk theory to allow for a larger class of risk models. Optional semimartingales are left-continuous with right-limit stochastic processes defined on a probability space where the usual conditions - completeness and right-continuity...

Mit diesem Bericht dokumentiert das Institut für Versicherungswesen (ivwKöln) seine Forschungsaktivitäten des vergangenen Jahres. Wir geben damit gegenüber der Öffentlichkeit und insbesondere den Freunden und Förderern des Instituts Rechenschaft über die geleistete Forschungsarbeit....

We leverage telematics data on driving behavior variables to assess driver risk and predict future insurance claims in a case study utilising a representative telematics sample. In the study, we aim to categorise drivers according to their driving habits and establish premiums that accurately...

This paper studies properties and applications related to the mixture of the class of distributions built by the Lehmann's alternative (also referred to in the statistical literature as max-stable or exponentiated distribution) of the form [𝐺(·)]𝜆, where 𝜆0 and 𝐺(·) is a continuous...

We obtain the upper and lower bounds for the ruin probability in the Sparre-Andersen model. These bounds are established under various conditions: when the adjustment coefficient exists, when it does not exist, and when the interarrival distribution belongs to certain aging classes....

Mit diesem Bericht dokumentiert das Institut für Versicherungswesen (ivwKöln) seine Forschungsaktivitäten des vergangenen Jahres. Wir geben damit gegenüber der Öffentlichkeit und insbesondere den Freunden und Förderern des Instituts Rechenschaft über die geleistete Forschungsarbeit....

The study of mortality is an ever-active field of research, and new methods or combinations of methods are constantly being developed. In the actuarial domain, the study of phenomena disrupting mortality and leading to excess mortality, as in the case of COVID-19, is of great interest....

The Danish fire loss dataset records commercial fire losses under three insurance coverages: building, contents, and profits. Existing research has primarily focused on the heavy-tail behaviour of the losses but ignored the relationship among different insurance coverages. In this paper, we aim...

This study proposes a new discrete distribution in the mixed Poisson paradigm to obtain a distribution that provides a better fit to skewed and dispersed count observation with excess zero. The cubic transmutation map is used to extend the exponential distribution, and the obtained continuous...

Mit diesem Bericht dokumentiert das Institut für Versicherungswesen (ivwKöln) seine Forschungsaktivitäten des vergangenen Jahres. Wir geben damit gegenüber der Öffentlichkeit und insbesondere den Freunden und Förderern des Instituts Rechenschaft über die geleistete Forschungsarbeit....

To manage market and longevity risk, Dr. Pfau shows how the use of life insurance and income annuities, as fixed income assets in a portfolio, can better hedge a retiree’s retirement-income needs as a portfolio volatility reduction tool

We extend the standard Cramér-Lundberg model to take the waiting time from occurrence to notification, and notification to settlement into account. Using this extended model and fixing a time of consideration, a prediction of the total outstanding liability of insurance claims that have...

This research studies a dynamic reinsurance model for an ambiguity-averse insurer. The insurer can manage its risk exposure through the purchase of reinsurance and the issuance of catastrophe bonds (CAT bonds) which are linked to an exogenous trigger index. The insurer worries about the veracity...

This paper introduces a target benefit pension (TBP) model that incorporates longevity risk and stochastic interest rate. Previous models have not considered the dynamic nature of remaining lifetime, and this paper proposes an Ornstein-Uhlenbeck (OU) process to simulate average remaining...

This tutorial gives an overview of SHAP (SHapley Additive exPlanation), one of the most commonly used techniques for examining a black-box machine learning (ML) model. Besides providing the necessary game theoretic background, we show how typical SHAP analyses are performed and used to gain...

Stochastic mortality models seek to forecast future mortality rates; thus, it is apparent that the objective variable should be the mortality rate expressed in the original scale. However, the performance of stochastic mortality models-in terms, that is, of their goodness-of-fit and prediction...

Modelling claim frequency and claim severity are topics of great interest in property-casualty insurance for supporting underwriting, ratemaking, and reserving actuarial decisions. Standard Generalized Linear Models (GLM) frequency-severity models assume a linear relationship between a function...

Mit diesem Bericht dokumentiert das Institut für Versicherungswesen (ivwKöln) seine Forschungsaktivitäten des vergangenen Jahres. Wir geben damit gegenüber der Öffentlichkeit und insbesondere den Freunden und Förderern des Instituts Rechenschaft über die geleistete Forschungsarbeit....

The Capitation Payment Unit (CPU) fnancing mechanism constitutes more than 70% of health spending in Colombia, with a budget allocation of close to 60 trillion Colombian pesos for the year 2022 (approximately 15.7 billion US dollars). This article estimates actuarially, using modern techniques,...

While the topics of risk aversion and utility theory have been discussed extensively in the academic literature on risk and insurance, this literature does not include a pedagogical discussion that is widely accessible for classroom use. This paper provides a practical introduction to risk...

This paper estimates pure–exporter premium, which captures the differences between pure exporters and general exporters in various firm characteristics. The data are Thailand’s firm-level data from three rounds of the industrial census in 2007, 2012, and 2017. The analysis finds positive...

This paper introduces and examines an intriguing puzzle arising from the market’s persistent tendency to overestimate the trajectory of spot interest rates resulting in lucrative cumulative long-term returns for net zero investments. We introduce a new metric called the “Hairy” premium to...

In this short note we discuss duration effects on the consistency of mean parameter and dispersion parameter estimators in exponential dispersion families (EDFs). Particular focus is on the situation corresponding to the standard generalised linear model assumptions where both the mean and...

This paper investigates an optimal reinsurance policy using a risk model with dependent claim and insurance premium by assuming that the insurance premium is random. Their dependence structure is modeled using Sarmanov’s bivariate exponential distribution and the Farlie–Gumbel–Morgenstern...

We defend, from a contractarian perspective, that the fair price of an insurance policy is the amount that the contracting parties agree when they are both equally uncertain about the insured event. Drawing on the approach developed by R. Sugden in The Community of Advantage, we answer two...