Sensitivity Analysis of Ruin of an Insurance Company in Ghana

TL;DR

This study analyzes how claim dependence affects ruin probability calculations for an insurance company in Ghana, highlighting the importance of considering dependence to avoid underestimating insolvency risk and informing better capital reserve strategies.

Contribution

It introduces a comparative sensitivity analysis of ruin probabilities under dependence and independence assumptions using copulas on Ghanaian insurance data, emphasizing the impact of claim dependence.

Findings

Dependence in claims leads to higher ruin probability estimates.

Assuming independence underestimates ruin risk when claims are dependent.

Motor insurance is the most profitable product, while fire insurance shows high dependency.

Abstract

An insurance company, as a risk bearer, is exposed to the likelihood of running into ruin. This is the situation where the initial surplus falls below zero. There is the need to find the required start-up capital to hedge against insolvency. Most researchers, irrespective of whether the test for claim dependency holds or not, assume claim independence in their computing of ruin probabilities to start up their initial capital. The objective of this study is to carry out comparative sensitivity analysis of ruin probability under both assumptions of dependence and independence, irrespective of whether the data exhibits independence or not, based on data from an insurance company in Ghana. Secondary data from an insurance company was obtained from the National Insurance Commission (NIC) for the period of 2013 to 2017. The study employed copulas to determine the claim dependence among the various insurance products and the company in general. The study concluded that when there is dependence in the claim data, computing the ruin probability based on the assumption of independence results in underestimation. Among the various insurance products, the most profitable insurance product was motor insurance, and Fire and Allied insurance exhibited the highest dependency. At a higher start-up capital, when claims are dependent, assuming independence in calculating the ruin probability results in a significant difference. Hence, it was recommended that insurance companies should adopt the assumption of dependence between the claims data as the initial reserves become larger, particularly for larger insurance companies, to avoid misleading results. Also, awareness of the perils and consequences of fire outbreaks and disasters should be raised to the general public to reduce the risk of frequent occurrence.