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Archives of Business Research – Vol. 11, No. 6
Publication Date: June 25, 2023
DOI:10.14738/abr.116.14871.
Berketis, N. G. (2023) A Chain-Ladder Analysis of P&I Claims - 2021. Archives of Business Research, 11(6). 43-59.
Services for Science and Education – United Kingdom
A Chain-Ladder Analysis of P&I Claims - 2021i
Nicholas G. Berketis
J. Kouroutis & Co. Ltd. Insurance and Reinsurance Brokers, Piraeus, Greece,
Frederick University, Cyprus, Athens University of Economics and Business,
Athens, Greece, Marine Insurance at Lloyd’s Maritime Academy
Keywords: claim, CL method, run-off triangle, claim reserving, P. & I.
According to the latest Market Review for 2021/2022 prepared by Lockton. 2 the latest financial
results from the International Group of P&I Clubs suggests that we are now in the full swing of
a hardening market with premium rises due to be requested over thenext year or, perhaps,
longer – whether this be due to individual Club performance or the renewal of the International
Group General Excess of Loss programme, or both.
These anticipated rises come at a time when the shipping market has only just showed signsof
improving and while operational expenses continue to rise – from the ongoing procedural
difficulties continuing from the pandemic to the exclusion of historically peripheral risks such
as cyber-attacks.
However, and despite these difficulties, the financial results of the P&I insurers are supporting
the Club’s argument that rises are required. Therein lies one of the unique traits of a mutual:
both the financial prosperity and burdens of the Clubs are shared across its members2.
The insurance industry, unlike other industries, does not sell products as such but promises.
An insurance policy is a promise by the Insurer to the Policyholder to pay for future claims
against an upfront received premium.
As a result, Insurers don’t know the upfront cost for their service, but rely on historical data
analysis and judgement to predict a sustainable price for their offering. In General Insurance
(or Non-Life Insurance, e.g., motor, property, and casualty insurance) most Policies run for a
period of 12 months. Nevertheless, the claims payment process can take years or even decades.
Therefore, not even the delivery date of their product is often unknown to Insurers.
Losses arising from casualty insurance can take a long time to settle and, even when the claims
are acknowledged, it may take time to establish the extent of the claims’ settlement cost. Claims
can take years to materialise. A complex and costly example is the claims from asbestos
liabilities, particularly those in connection with mesothelioma and lung damage arising from
prolonged exposure to asbestos. A research report by a working party of the Institute and
Faculty of Actuaries estimated that the un-discounted cost of UK mesothelioma-related claims
to the UK Insurance Market for the period 2009 to 2050 could be around £10bn. The cost
for asbestos related claims in the US for the worldwide insurance industry was estimated to be
around $120bn in 2002.
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Archives of Business Research (ABR) Vol. 11, Issue 6, June-2023
Services for Science and Education – United Kingdom
Thus, it should come as no surprise that the biggest item on the liabilities side of an Insurer’s
balance sheet is often the provision or reserves for future claims payments. Those reserves can
be broken down in case reserves (or outstanding claims), which are losses already reported to
the insurance company and losses that are incurred but not reported (IBNR) yet.
The analysis is based on most recent version of R (Version 4.1.2 – 01st November 2021), an
integrated language and environment for statistical computing and graphics. R provides a wide
variety of statistical and graphical techniques.
The estimated cost of notified pool claims (in USD 000,000) is as follows:
YEAR 12M 24M 36M 48M 60M 72M 84M 96M 108M 120M
2011/12 2310 2779 2808 2896 2893 2887 2844 2812 2802 2799
2012/13 3686 4539 4670 4651 4463 4186 4036 3927 3834 NA
2013/14 2798 3270 3640 3649 4116 4086 4231 4306 NA NA
2014/15 1796 1936 2045 2158 2213 2129 2065 NA NA NA
2015/16 1984 2766 2840 2827 2914 2955 NA NA NA NA
2016/17 840 1259 1450 1365 1402 NA NA NA NA NA
2017/18 2272 2696 2897 3105 NA NA NA NA NA NA
2018/19 3061 4558 4900 NA NA NA NA NA NA NA
2019/20 2592 4417 NA NA NA NA NA NA NA NA
2020/21 4629 NA NA NA NA NA NA NA NA NA
This triangle shows the known values of loss from each origin year and of annual evaluations
thereafter. For example, the known values of loss originating from the 2013/14 exposure
period are 2798, 3270, and 3640 as of year ends 2013, 2012, and 2011, respectively. The latest
diagonal – i.e., the vector 2799, 3834, . . . 4629 from the upper right to the lower left – showsthe
most recent evaluation available.
The column headings – 1, 2, . . ., 10 – hold the ages (in years) of the observations in the column
relative to the beginning of the exposure period. For example, for the 2014/15 originyear, the
age of the 2045 value, evaluated as of 20/02/2018, is three years.
The objective of a reserving exercise is to forecast the future claims development in the bottom
right corner of the triangle and potential further developments beyond development
age 10. Eventually, all claims for a given origin period will be settled, but it is not always
obvious to judge how many years or even decades it will take.
We speak of long and short tail business depending on the time it takes to pay all claims.
In order proceed with our analysis, we first plotted the data to get an overview. Figure 1 that
follows shows the claims development chart for the past 10 years.
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Berketis, N. G. (2023) A Chain-Ladder Analysis of P&I Claims - 2021. Archives of Business Research, 11(6). 43-59.
URL: http://dx.doi.org/10.14738/abr.116.14871
Figure 1 – Claims Development Chart for the past 10 Years
CHAIN-LADDER METHODS
The classical chain-ladder is a deterministic algorithm to forecast claims based on historical
data. It assumes that the proportional developments of claims from one development periodto
the next are the same for all origin years.
Basic Idea
Most commonly as a first step, the age-to-age link ratios are calculated as the volume weighted
average development ratios of a cumulative loss development triangle from one development
period to the next Cik, i, k = 1, . . ., n.
fk=
∑i=1
n−kCi, k+1
∑i=1
n−kCi,k
[1] 1.3224612 1.0607907 1.0147912 1.0259318 0.9785529 0.9915713 0.9940599 0.9847158
0.9989293.