Modelling claim reserves using 'inflated' Basic Chain Ladder Method

Most of the Actuarial analyst they don't feature in the inflation aspect while using this method, I get the reason, reserve overestimation!!! Most probably yeah. Kenyactuary  modified the calculation of the development factors such that instead of using weighted average a method which incorporates inflation aspect is used in the code part. 

INTRODUCTION

Risk is a complex issue that cannot be merely estimated without having to think about loss critically as a  random variable whereby in case of a loss then it can be ‘catastrophic’. The only solution one would opt for is to transfer the same risk to another entity. The role of transferring risk is played by insurance companies through an individual buying an insurance policy whereby the individual will pay periodic payments called premiums, upon loss the insured (individual) will be indemnified by the insurer (insurance company). An insurance policy is a contract, usually written, between an insurer and the insured which lasts for a given period of time according to a type of policy. The general explanation of the contract is that upon occurrence of a loss under the risk insured the insurer indemnifies the insured under the stated terms and conditions of the policy after a claim has been made and assessed. Policies are usually categorized into two, namely non-life and life insurance policies, non-life policies are the ones that don’t involve life for instance, motor insurance policies while life policies involve life for example, whole life, term assurance, and endowment policies. Currently, motor insurance has greatly grown due to growth in the motor industry. Motor insurance usually deals with motor vehicles, that is, personal vehicles, public service vehicles, and motorbikes among other insurable motors.

In Kenya the public service sector contributes to a higher percentage of the insurance policies since most of insurance companies’ main policies are motor insurance policies which they really advertise for in different social media platforms, some of these companies are Directline, Kenya Orient, Heritage, Invesco, Jubilee and Amaco among others. Bearing in mind that it is a government policy for every vehicle to have an insurance policy, definitely potential insured will definitely increase and usually, this is a joy to motor insurance companies, but the problem arises while settling claims. Sometimes, the insurer faces the problem of delay in claim reporting upon occurrence and there is also a delay in settlement of the reported claims, mostly due to unavoidable reasons. To address this problem, it’s important for insurance companies to know what to reserve at a regular interval so as to meet the demands of the claims arising from incidents that have taken place, otherwise, the company is prone to sustainability risk due to customer-company relationships.

In Motor insurance, it’s a challenge to determine the amount of loss that has occurred and may prompt further investigation by risk assessors which might lead to a delay between the time of claim occurrence and the time of claim payment. Most firms set the reserves and include them in the financial statement and represent the expected expense by the insurer. They are vital because they are applied in measuring the company’s financial health. However, inaccurate reserve estimation can present a false image of the financial position of the insurance company hence there is a need for proper and accurate estimation of reserves based on information and kind of data that is available on that claim. Therefore, motor insurance companies should come up with more effective models to assess the expected loss that is to be met based on the policies that originated the year before. This will enable the motor insurance companies to set up enough and reasonable resources to meet future obligations to the insured.

Claims occurs almost daily, for example in Kenya the year 2022 recorded 21,757 road accident casualties, representing a 5.5 per cent increase from the 20,625 deaths reported in 2021, this translates to possible number of claims made every year by the insured under motor insurance policies. Some are reported but others are not reported on the same day due to various reasons. These reasons may be due to normal delays in claim reporting or due to challenges in determining and quantifying the size of the claim and many more other reasons. Whatever assurance we have is that the claims have to be addressed if not settled no matter how long it takes. These claims which are not yet known to the insurer due to delay in reporting but for which liability is believed to exist at the reserving time are known as Incurred but not Reported claims. Data from historical claim experience are the ones that are applied in the estimation of future payments. The challenge is to identify the most appropriate model that can accurately give the estimates that will be used effectively by motor insurance companies and brokers so as to make the right decisions on claim reserves. This is because overestimation of claim reserves will greatly affect investment negatively because much money will be used for reserving instead of income generation in other forms similarly, underestimation of reserves will negatively impact the insurer since the company may not be able to compensate the insured or settle any claims that has occurred. Using data obtained from historical experience, the actuary can obtain estimates on the prediction of outstanding claim risk. Some of the most used methods for claim reserving are collective risk models, individual risk models, and Basic chain ladder models among others.

Claim settlement process

The main goal of insurance is to settle claims. So, people get insurance to pay a regular amount called premiums. If something bad happens and causes a loss, the insurance company agrees to pay for it during a certain time. But, to get this payment, the insured person needs to follow a specific process. This process is called the claim settlement process. In general insurance, the claim settlement usually happens in following stages.

However, claim settlement may take several years until it is finally settled. This is mainly due to the following reasons.

1. Delay in Claim Reporting - The time between the occurrence of the claim and the time of reporting that involves notification at the concerned motor insurance company.

2. Delay in Claim settlement - Time interval between reporting date and final settlement due to reasons such as Severity of the claim, recovering process and the decision from court etc.

Incurred but not reported claims (IBNR) in motor insurance

The decision to select the most effective and suitable model for estimating outstanding claims, including Reported but Not Settled (RBNS) and Incurred but Not Reported (IBNR) claims is crucial for safeguarding the financial stability of insurance companies, particularly in the context of motor insurance. In Motor Insurance, claims associated with policyholders that occur in a given year are often reported to the insurance company in subsequent years or even many years later, especially in most Kenyan insurance companies. However, there can be delays in payouts for various reasons, hence necessary to establish sufficient reserves to cover these future claims that may arise. The claim reserve in this context consists of reserves for both known and unknown claims. The loss reserve in motor insurance is divided into two categories, the reported claims and unreported claims that have occurred but are not yet known to the insurance company. Therefore, the total reserve can be categorized as the reserve for known claims and unknown claims.

Reported but not settled (RBNS) claims in motor insurance 

These refer to claims which have been reported but remain unpaid beyond the conclusion of the insurance company's financial year. As of the end of the financial year, both IBNR (Incurred but Not Reported) and RBNS (Reported but Not Settled) claims have not been settled by the insurer.

 

Statement of problem

In recent years’ motor insurance industry has grown rapidly in Kenya, a contribution by both local and foreign firms. Due to this growth, there is also a rising complaint of some insured on the delay of the insurers (motor insurance companies) in indemnifying claimants, this leads to piling up of unsettled claims. To solve this problem there is a need for motor insurance companies to set aside a reserve to pay claims whenever they arise. This can be achieved by choosing an appropriate, data-based, and sophisticated model for estimating claims to avoid underestimation and overestimation of reserves. Most upcoming motor insurance agencies and brokers set hypothetical values as reserves with limited quantitative risk knowledge due to lack of experience which poses a risk of insolvency. This therefore prompted us to do a study on the Basic Chain Ladder model which is a prominent actuarial loss reserving model that computes incurred but not reported claims which is a common occurrence in the motor insurance industry. We will use the chain Ladder method to construct an automated R programming model to analyze and predict the reserves.

Objectives

General Objective

To develop an automated R programming model that can be used to analyze and predict the aggregate claim reserve in motor insurance. 

Specific Objectives

1. To use Basic Chain Ladder method to construct a model to estimate the ultimate motor insurance claim amounts in each underwriting year

2. To compute IBNR and claims that are yet to occur as per the current calendar year using the constructed model.

3. Test the model using the data from Ghana Reinsurance Company.

Limitations and advantages of Basic Chain Ladder Model

 There are several limitations of this model which include:

1. This method may be sensitive to extreme values (outliers) which can lead to inaccurate projections. 

2.  The method may not capture structural changes in the underlying claims process leading to biased projections.

3. The method requires a sufficient amount of high-quality historical data to establish credible development patterns which may not always be available.

However, this model has its own advantages which include: 

1. The method is simple and easy to understand.

2. It is easy to interpret making it easy for decision-making in companies.

Assumptions of the Study 

1. Claim settlement is done over a fixed number of a given development years.

2. The behavior of claims amounts will follow a predictable trend based on historical data

3. The accuracy of historical claims data is assumed, as the run-off triangle relies heavily on past patterns.

4. The process of handling and settling claims will remain stable without significant changes.

5.  The model assumes the ultimate claims include IBNR, those that are yet to occur and those that have been reported but not paid.

Data description

In this work, we have made use of data from one of the reinsurance companies in Kenya. The data was obtained from Ghana Reinsurance Company and consists of valuation classes which include marine, fire, accident, motor and other approved products. We have used the motor valuation class data from 2013 – 2020.

4.2 Data analysis tools

In this research, we employed R version 3.6.2 and Microsoft excel to carry out most of the data analytics. R was widely used to be specific.

4.3 General data analysis

The data was presented in an incremental run off triangle. We grouped the claims data according to the underwriting year hence the development year (delay) is booking year minus underwriting year where booking year is the year when the claim was reported. We achieved data presentation using Microsoft excel pivot tables as shown below: 

Origin	Dev0	Dev1	Dev2	Dev3	Dev4	Dev5	Dev6	Dev7
2013	446122.9	3919914	508246.4	2699258	27605.5	0	0	655923.4
2014	3153563	2969464	3466989	271371.4	0	145792.5	2449659
2015	1736054	4413912	3958945	1346774	432750	1585503
2016	2012000	8729081	2632613	160506.7	448362.1
2017	855546.6	2012971	116146	188359.3
2018	1773781	4454882	2247665
2019	7835087	3230450
2020	1972552

figure 1: incremental run off triangle

Step by step application of the Basic Chain Ladder Model

Step 1:

a. Uploading the data

We uploaded the incremental run off triangle in R posit cloud. After uploading and viewing the output is as shown:

Figure 1: Incremental run off triangle

b. Graphical representation 

Using R functions, we plotted incurred claims against the origin year/underwriting year. The graph shows how the claim amount develops in each development year from 2013 to 2020. The output is as shown below: 

Figure 2: Graphical representation of claim development

Step 2: 

We transformed the incremental run off triangle to cumulative run off triangle so as to use the cumulative approach to forecast the claim amounts. The output is as shown below:

Figure 2: Cumulative run off triangle

Step 3: 

We calculated link ratios (age to age factors) for each underwriting year(origin) and hence calculated the average column wise to give the development factors for each development year. The output is as shown below:

Figure 3: Underwriting year link ratios

Figure 4: Development factors for development years

Step 4:

Using the development factors for the development years we were able to forecast the values of the lower part of the run off triangle, this shows the forecasted cumulative claim amounts of the respective underwriting year and the development year. The output is as shown below:

Figure 5: The forecasted run off triangle

Step 5:

We forecasted the ultimate claim amount for each underwriting year for that year which also achieves our objective number one. 

Figure 6: The forecasted ultimate claims

The ultimate total reserve is the addition of IBNR and those claims that are yet to occur and outstanding reported claims. The figure below shows the IBNR and those claim amounts that are yet to occur for each underwriting year and their totals by doing this we achieved objective two. The outputs are as shown:

Figure 7: Past Claim amounts

We calculated the IBNR by getting the difference between the ultimate claims ad past claims. The outputs are as shown:

Figure 8: Forecasted IBNR and claims that are yet to occur

Need a code to do this? 

By Mutharimi Phineas

(CEO, The Kenyactuary)