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Analysis of Aggregate Claims Distributions in General Insurance

Abstract

The study analyses aggregate claims distributions in general insurance, with emphasis on the statistical behaviour of total claims arising from an insurance portfolio over a specified period. Aggregate claims represent the combined financial impact of individual claims and are important in actuarial analysis because they provide a basis for assessing overall loss exposure, premium requirements, reserve adequacy, and financial risk. Understanding the distribution of aggregate claims is therefore essential for effective insurance risk assessment and financial planning. The study will examine the distributional characteristics of aggregate claims in general insurance and assess how claim frequency and claim severity contribute to variations in total losses. It will investigate the pattern of aggregate claims and determine the extent to which statistical models can adequately represent observed insurance loss experience. The study will also consider the usefulness of aggregate claims distributions in actuarial decision-making and insurance risk management. The study will focus on the frequency-severity framework for aggregate claims modelling. Probability distributions such as the Poisson and negative binomial distributions may be used to model claim frequency, while appropriate severity distributions may be applied to individual claim amounts. These components will be combined using aggregate loss modelling techniques to examine the resulting distribution of total claims and its key characteristics, including expected losses and variability. A quantitative research approach will be adopted for the study. Historical general insurance claims data containing claim counts and individual claim amounts will be analysed over a defined period. Descriptive statistics, probability distribution fitting, goodness-of-fit tests, and aggregate claims modelling techniques will be employed. The estimated aggregate distributions will be assessed based on their ability to represent the observed claims experience and provide useful estimates of total insurance losses. The study is expected to reveal that aggregate claims distributions vary according to the underlying frequency and severity characteristics of insurance losses. The findings may indicate that appropriate combinations of frequency and severity distributions provide more reliable representations of aggregate claims experience. The analysis may also show that portfolios with greater variation in claim frequency or severity exhibit higher uncertainty in aggregate loss estimates. The findings are expected to provide useful information for insurance companies and actuaries in assessing overall claims exposure and estimating potential financial obligations. The study may assist insurers in improving premium estimation, reserve determination, capital planning, and risk management practices. It may also provide a basis for selecting appropriate probability distributions for modelling aggregate claims in general insurance portfolios. The study concludes that aggregate claims distributions provide an important framework for understanding the total loss experience of general insurance portfolios. It is therefore recommended that insurers regularly analyse claims frequency and severity and apply appropriate probability distributions and actuarial techniques when modelling aggregate losses. Proper analysis of aggregate claims distributions may contribute to more accurate loss estimation, improved premium adequacy, and effective insurance risk management.

Keywords: Aggregate claims distributions, general insurance, aggregate loss modelling, claim frequency, claim severity, actuarial modelling, probability distributions, insurance losses, claims experience, Poisson distribution, negative binomial distribution, loss distribution, expected claims, reserve estimation, insurance risk management.