An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company

Soontorn Boonta,Somchit Boonthiem

doi:10.1155/2019/2191509

Soontorn Boonta, Somchit Boonthiem

Open Access

https://doi.org/10.1155/2019/2191509

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Abstract

Catastrophe is a loss that has a low probability of occurring but can lead to high-cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare the parameter estimation using a direct search method with other frequently used methods, such as the least squares method, the maximum likelihood estimation, and the method of moments. The results show that the direct search method approximates the parameters more precisely than other frequently used methods (to four-digit accuracy). Second, we approximate the minimum initial capital (MIC) a reinsurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part. Finally, we show MIC with varying the premium rate.

Highlights

The risks of an insurance company can be assessed based on disasters of varying severity
The results showed that the direct search technique gave a more precise estimation than the least squares method, the maximum likelihood estimation, and the method of moments
This work presents the use of the direct search technique to estimate the parameters of a Weibull distribution

Summary

Introduction

The risks of an insurance company can be assessed based on disasters of varying severity. Chan and Zhang [12] have studied a discrete time surplus process such as claim time Tn = n (claims which occur every day) They proposed recursive and explicit formulae of the ruin probabilities which are in the form n. The results of the study led to the proposal of two upper bounds of ruin probability under a discrete time risk model for reinsurance by generalizing the classical model in terms of two controlling factors: proportional reinsurance and investment. The second part is a simulation to calculate the ruin probability of the surplus process under the condition that a reinsurance company can invest in risk-free assets (bonds or fixed accounts). We approximate the minimum initial capital (MIC) an insurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part

Materials and Methods

Weibull Parameter Estimation

Method of moments

Part I

Part II

Conclusion and Suggestion