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Estimation of Aggregate Claims Using Compound Probability Models

Abstract

The study examines the estimation of aggregate claims using compound probability models, focusing on the application of actuarial probability techniques to estimate the total claims arising from an insurance portfolio over a specified period. Aggregate claims represent the combined financial value of individual claims and are important in insurance because they provide a basis for estimating expected losses, determining premium requirements, assessing reserve needs, and managing financial risk. Reliable estimation of aggregate claims is therefore essential for sound actuarial and insurance decision-making. The study will investigate the use of compound probability models in estimating aggregate insurance claims. It will examine how the frequency of claims and the monetary severity of individual claims can be combined to determine the distribution and expected value of total claims. The study will also assess the usefulness of compound models in representing variations in aggregate claims and improving the accuracy of actuarial loss estimates. The study will focus on compound probability techniques that combine separate probability distributions for claim frequency and claim severity. A suitable frequency distribution, such as the Poisson or negative binomial distribution, may be combined with an appropriate severity distribution for individual claim amounts. The resulting compound models will be used to estimate expected aggregate claims, variance, and other measures of insurance loss variability. A quantitative research approach will be adopted for the study. Historical insurance claims data containing claim counts and individual claim amounts will be analysed over a defined period. Descriptive statistics, probability distribution fitting, parameter estimation, and compound distribution techniques will be applied to the data. The estimated aggregate claims will then be evaluated to determine the suitability and reliability of the selected compound probability models. The study is expected to reveal that compound probability models provide a useful framework for estimating aggregate insurance claims by incorporating both claim frequency and claim severity. The findings may indicate that differences in the assumed frequency and severity distributions can produce variations in aggregate claim estimates. The analysis is also expected to show that appropriate model selection can improve the representation of aggregate claims and reduce uncertainty in actuarial loss estimation. The findings are expected to provide useful information for actuaries and insurance companies in estimating potential aggregate losses and evaluating insurance portfolio risk. The study may assist insurers in improving premium estimation, reserve determination, capital planning, and claims forecasting. It may also provide a practical basis for applying compound probability models to insurance portfolios where both the number and size of claims contribute to total financial exposure. The study concludes that compound probability models provide an important actuarial framework for estimating aggregate claims because they integrate claim frequency and claim severity into a single loss model. It is therefore recommended that insurance companies carefully analyse historical claims experience and select appropriate probability distributions when developing compound aggregate claims models. Effective application of these models may contribute to more reliable loss estimates, improved premium adequacy, and stronger insurance risk management.

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