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Effect of Claim Deductibles on Insurance Loss Distribution Modelling

Abstract

Claim deductibles represent the portion of an insured loss that is borne by the policyholder before the insurer becomes responsible for the remaining claim amount. They are an important feature of insurance contracts and can influence the amount and distribution of losses ultimately borne by insurers. Accurate consideration of deductibles is therefore relevant to actuarial loss modelling, risk assessment, premium estimation, and insurance portfolio management. The study examines the effect of claim deductibles on insurance loss distribution modelling. It will assess how different deductible levels influence the statistical distribution of losses retained by insurers. The study will also examine the relationship between deductible amounts, claim severity, loss frequency, retained losses, and the resulting characteristics of insurance loss distributions. The study will focus on claim deductibles, loss distributions, claim severity, claim frequency, retained losses, deductible levels, aggregate losses, and actuarial risk measures. Probability distributions and actuarial loss models will be applied to represent insurance losses under different deductible structures. Comparative and sensitivity analyses will be used to examine changes in the shape, variability, and expected value of loss distributions as deductible levels change. A quantitative research approach will be adopted for the study. Relevant insurance claims data, including individual claim amounts, claim frequencies, policy exposure, deductible levels, and historical loss experience, will be considered. Descriptive statistics, probability distribution fitting, actuarial loss modelling, comparative analysis, and sensitivity analysis will be used to examine the effect of claim deductibles on insurance loss distribution modelling. The study is expected to show that claim deductibles can materially influence the estimated distribution of insurer losses. Higher deductible levels may reduce the losses retained by insurers and alter the frequency and severity characteristics represented in the loss distribution, while lower deductibles may result in greater retained losses. The extent of these changes may depend on the underlying claim severity distribution, deductible structure, claim frequency, and characteristics of the insurance portfolio. The study is expected to provide useful information for actuaries, insurers, underwriters, pricing analysts, and risk managers. The findings may support more accurate loss distribution modelling, premium determination, deductible design, risk assessment, claims analysis, and evaluation of insurer loss exposure. The study may also assist insurance companies in selecting appropriate actuarial models for portfolios with different deductible structures. The study concludes that claim deductibles are an important consideration in insurance loss distribution modelling. It is therefore recommended that insurers incorporate applicable deductible structures into actuarial loss models, evaluate alternative deductible levels through sensitivity analysis, and regularly review claims data to improve the accuracy of estimated loss distributions.

Keywords: Claim deductibles, insurance loss distribution, loss distribution modelling, deductible levels, claim severity, claim frequency, retained losses, aggregate losses, actuarial modelling, probability distributions, insurance risk, loss estimation, premium determination, actuarial analysis, insurance claims.