### 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 |
---|---|

Pages (from-to) | 233-239 |

Number of pages | 7 |

Journal | Journal of Mathematics and Statistics |

Volume | 6 |

Issue number | 3 |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

- Aggregate losses
- Compound poisson-pareto
- Simulation

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Journal of Mathematics and Statistics*,

*6*(3), 233-239.

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

Research output: Contribution to journal › Article

*Journal of Mathematics and Statistics*, vol. 6, no. 3, pp. 233-239.

}

TY - JOUR

T1 - Approximation of aggregate losses using simulation

AU - Mohamed, Mohamed Amraja

AU - Razali, Ahmad Mahir

AU - Ismail, Noriszura

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Aggregate losses

KW - Compound poisson-pareto

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=77956793094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956793094&partnerID=8YFLogxK

M3 - Article

VL - 6

SP - 233

EP - 239

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 3

ER -