1.1 Background of the study
Motor Insurance which is sometimes also referred to as automobile insurance is a form of security which is purchased to protect the buyer of the product from future loss (Awunyo-Vitor, 2012). The National Insurance Commission (NIC) described the aim of motor insurance as providing compensation for loss or damage to one’s motor vehicle. These compensations, usually referred to as claims, however aims at providing compensation for injury or death to third parties arising from vehicular accidents or the car owner in the event of loss arising out of
theft of the vehicle or loss from damage caused by re (NIC, 2015). General insurance under which motor insurance falls is perhaps the fastest growing area for Actuaries thus resulting in huge amount and number of claims (Achieng, 2010). This however calls for claim actuaries to be more concerned with both the claim amount and number since they are likely to have large control on the nances of the rm. Due to the fact that insurance is data driven, a lot of insurance companies employ large numbers of actuarial analysts to understand
the large volumes of claims data. Unfortunately, actuaries managing claims do not concern themselves with the occurrence of claims themselves but the amount
the insurance industry will have to pay than the exact situations which gives rise
to the claim numbers (Boland, 2006).
A much critical attention to both claim numbers and amounts will enable claim
managers to enable them develop suitable models which will predict future claim
amounts and numbers. This is termed reserve techniques. This is sometimes
referred to a loss reserves since they are used to predict and hedge against future
losses which will arise from claims from the policy. Established reserving
techniques seek to address the challenge of predicting future claims development
through a top-down approach (Orr, 2007). These methods normally consider the
overall development of the portfolio in previous years and assume that it will
follow a similar trend in the future years. In practice, factors surrounding the
historical factors will be taken into consideration for the development years.
Techniques such as the basic chain ladder, which is one of the simplest as it was
developed in the pre-computer age and does not involve specialized software (Orr,
2007). Other stochastically developed techniques which uses proportions in estimating
claim developments. In this study, a multistate model will be considered
to explore the idea that the claims development of an insurance portfolio, often
presented as a attened s-curve of incurred (reported) or paid claims over time.
The application of multistate models to actuarial problems was rst introduced
by Hoem (Orr, 2007). Signicant contributions to the analysis of present values
in a multistate model framework were made by Waters (1984). Few studies have
been conducted over the years on the Markov loss reserve model which involves
states such as the Incurred but not reported (IBNR), Reported but Not Settled
(RBNS) and Settled (S). Others include states such as Reported but No Case
Reserve and Reported and Case reserve. These could either be a time inhomogeneous
markov jump chain or time inhomogeneous Poisson process (Hesselager,
1.2 Problem Statement
Claims arising from motor insurance policies are usually the most incurred which
gives rise to large volumes of data. Thus for the development of a suitable model,
the attention of the claim actuaries should not only be on the occurrence of claims
for future predictions but also the number of claims (Orr, 2007).
At Vanguard Assurance Company limited, motor policy records an over-whelming
number of claims in any given period. It is for this reason that there is a need to
t a model that does not just focus on the claims being paid to the clients but
also the number of claims. Fitting this model enables the claim actuaries to best
forecast future expected claims and also make reserves which will be adequate to
curb these losses.
In most companies, it takes a longer time to settle a reported claim than the
time it is reported Orr (2007) thus creating a huge back lock of ‘outstanding’
claims. It is however a problem when all these claims are not settled in the same
accident year but are transferred and added to the next accident year, which is
most often referred to as development years.
The Markov model provides a relatively simpler approach to modeling loss reserves
as compared to the traditional chain ladder approach (Hesselager, 1995).
Thus the need to know their distribution will aid the process since it will aid
the actuary in summarizing and modeling large amounts of claims data. These
distributions however are very important to actuaries (Raz, 2000).
To explore how simple common process may underline the development of claims
arising from motor insurance contracts.
1.3.1 Specic Objectives
The specic objectives of the study are;
1. To estimate the transition intensities between claim development model
2. To derive the closed-form expressions for the expected numbers of losses
and claims in each state at each point in time, t, which describes the expected
development prole for the model.
3. To use the multistate model to simulate expected claim counts in the accident
and development years.
4. To identify the accident year after which claims are fully run o
1.4 Research Hypothesis
H0 : There is no underlying process for the emergence of claims from a portfolio
of motor insurance contracts.
H1 : There is an underlying process for the emergence of claims from a portfolio
of motor insurance contracts.
1.5 Signicance of the study
The motor insurance policy is very essential because the Motor Vehicles (Third
Party Insurance) Act, 1958 (as amended) demands that whoever uses a vehicle on
any public road must take insurance to cover his liabilities to others arising out of
the use of the vehicle. Thus the general insurance, which covers motor insurance,
section of the insurance companies is their largest wealth pulling sectors (NIC,
This results in large number of claims and claim amounts in each year round.
Claim actuaries who have the task of ensuring claims are taken care of also have
the task of advising management on the amount needed to be reserved for future
claims. This study intends to provide claim managers an approach to modeling
claim reserves which uses volumes of claims in modeling and not just claim
amounts. This method is an appropriate method for large number of claims as in
this case. Subsequently, it will help claim actuaries to know how much and when
claims will be made in the future and also help estimate future losses.
1.6 Scope of Study
This research will cover the general business, particularly motor insurance policies
for all kinds (commercial or private) and policy types (comprehensive, third
party …) of Vanguard Assurance. The number of claims which are not reported
(IBNR), those yet to be settled (RBNS) and those settled (S)
1.7 Limitations of the study
The study had the following limitations;
1. The data organization structure created a limitation as to the number of
states the process (claim development) goes through before nally being
2. Studies performed in this area using this model were limited thus limited
literature on claim development process.
3. Time allocated for the research limited the research to just motor insurance
and in just one insurance company.
4. Data was also a limitation to the study since claims data for just one year
The thesis will be presented in ve major chapters. Chapter one is the introduction
which presents the background to the study, statement of the problem,
objective of the study, signicance of the study, scope of the study and the limitations
of the study. Chapter two will present review of relevant literature and
comprises theoretical framework and dierent perspective of researchers of the
problem related to reserve models. The methodology to achieve the objectives
is outlined in chapter three and here the relationships between the three fundamental
trac variables are developed. Chapter four presents the data analysis,
modeling results and the accompanying discussions. The summary of nding conclusions
and recommendations are presented in chapter ve, then the References
1.9 Denition of Terms
1. Claim – a demand or request for something considered one’s due.
2. Loss – A loss is the injury or damage sustained by the insured in consequence
of the happening of one or more of the accidents or misfortunes
against which the insurer, in consideration of the premium, has undertaken
to indemnify the insured.
3. Random Variable-A function that associates a unique numerical value
with every outcome of an experiment.
4. Reserve-Provisions for future liabilities which indicate how much money
should be set aside now to reasonably provide for future pay-outs.
5. Severity-This can either be the amount paid due to a loss or the size of a
6. Model-An imitation of a real world system or process.
7. Actuary-An actuary is a business professional who deals with the measurement
and management of risk and uncertainty.
8. Maximum Likelihood Estimate-is a method of estimating the parameters
of a statistical model given data.
9. Insurance-is the equitable transfer of the risk of a loss, from one entity to
another in exchange for money. It is a form of risk management primarily
used to hedge against the risk of a contingent, uncertain loss. An insurer,
or insurance carrier, is selling the insurance; the insured, or policyholder, is
the person or entity buying the insurance policy.
1.10 Chapter Summary
General insurance under which motor insurance falls is perhaps the fastest
growing area for Actuaries thus resulting in huge amount and number of
claims (Achieng, 2010). This however calls for claim actuaries to be more
concerned with both the claim amount and number since they are likely to
have large control on the nances of the rm (Boland, 2006). Companies
controlling large amount of claims need to be concerned about a model
for claim numbers also. The purpose of this study was however to explore
how simple common process may underlie the development of claims arising
from motor insurance contracts of Vanguard Assurance Company Limited.
The study considers claims in three states; IBNR, RBNS and PAID. The
following chapter reviews relevant literature on multistate reserving models
and other reserving models. It will also explain theories underlying this