# Approximation of aggregate losses using simulation

Mohamed Amraja Mohamed, Ahmad Mahir Razali, Noriszura Ismail

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

Problem statement: The modeling of aggregate losses is one of the main objectives in actuarial theory and practice, especially in the process of making important business decisions regarding various aspects of insurance contracts. The aggregate losses over a fixed time period is often modeled by mixing the distributions of loss frequency and severity, whereby the distribution resulted from this approach is called a compound distribution. However, in many cases, realistic probability distributions for loss frequency and severity cannot be combined mathematically to derive the compound distribution of aggregate losses. Approach: This study aimed to approximate the aggregate loss distribution using simulation approach. In particular, the approximation of aggregate losses was based on a compound Poisson-Pareto distribution. The effects of deductible and policy limit on the individual loss as well as the aggregate losses were also investigated. Results: Based on the results, the approximation of compound Poisson-Pareto distribution via simulation approach agreed with the theoretical mean and variance of each of the loss frequency, loss severity and aggregate losses. Conclusion: This study approximated the compound distribution of aggregate losses using simulation approach. The investigation on retained losses and insurance claims allowed an insured or a company to select an insurance contract that fulfills its requirement. In particular, if a company wants to have an additional risk reduction, it can compare alternative policies by considering the worthiness of the additional expected total cost which can be estimated via simulation approach.

Original language English 233-239 7 Journal of Mathematics and Statistics 6 3 Published - 2010

### Fingerprint

Approximation
Simulation
Compound Distribution
Insurance
Compound Poisson
Pareto Distribution
Poisson distribution
Probability Distribution
Alternatives
Requirements
Costs
Modeling

### Keywords

• Aggregate losses
• Compound poisson-pareto
• Simulation

### ASJC Scopus subject areas

• Mathematics(all)
• Statistics and Probability

### Cite this

Approximation of aggregate losses using simulation. / Mohamed, Mohamed Amraja; Razali, Ahmad Mahir; Ismail, Noriszura.

In: Journal of Mathematics and Statistics, Vol. 6, No. 3, 2010, p. 233-239.

Research output: Contribution to journalArticle

Mohamed, Mohamed Amraja ; Razali, Ahmad Mahir ; Ismail, Noriszura. / Approximation of aggregate losses using simulation. In: Journal of Mathematics and Statistics. 2010 ; Vol. 6, No. 3. pp. 233-239.
title = "Approximation of aggregate losses using simulation",
abstract = "Problem statement: The modeling of aggregate losses is one of the main objectives in actuarial theory and practice, especially in the process of making important business decisions regarding various aspects of insurance contracts. The aggregate losses over a fixed time period is often modeled by mixing the distributions of loss frequency and severity, whereby the distribution resulted from this approach is called a compound distribution. However, in many cases, realistic probability distributions for loss frequency and severity cannot be combined mathematically to derive the compound distribution of aggregate losses. Approach: This study aimed to approximate the aggregate loss distribution using simulation approach. In particular, the approximation of aggregate losses was based on a compound Poisson-Pareto distribution. The effects of deductible and policy limit on the individual loss as well as the aggregate losses were also investigated. Results: Based on the results, the approximation of compound Poisson-Pareto distribution via simulation approach agreed with the theoretical mean and variance of each of the loss frequency, loss severity and aggregate losses. Conclusion: This study approximated the compound distribution of aggregate losses using simulation approach. The investigation on retained losses and insurance claims allowed an insured or a company to select an insurance contract that fulfills its requirement. In particular, if a company wants to have an additional risk reduction, it can compare alternative policies by considering the worthiness of the additional expected total cost which can be estimated via simulation approach.",
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