Excited to share our recent participation in 34th General Arab Insurance Federation (GAIF) Conference 2024 in the beautiful capital of the Sultanate of Oman, Muscat. We were honored to have the opportunity to meet and interact with industry leaders from across the region.

Asia Reinsurance Brokers (ARB) in cooperation with PT Reasuransi Nasional Indonesia (Nasional Re) organized a “Treaty Pricing Training Session” from 13 June 2023 to 15 June 2023. The attendees included Mr Saliya Jinadasa (Senior Divisional Director – Asia Reinsurance Brokers Pte Ltd) as the main speaker at this event, Mr Michael Seward (President Director – PT Asia Reinsurance Brokers Indonesia), Bpk Wayan Sumendra (Director – PT Asia Reinsurance Brokers Indonesia), Bpk Defit (Technical Director – Nasional Re), Bpk Roland Silaban (Head of Treaty Division – Nasional Re), as well as other participants from Nasional Re and PT Asuransi Kredit Indonesia (Askrindo).

Going Beyond Tradition – Reinsurance Treaty Pricing with Piecewise Pareto Distribution Typically, non-proportional treaty pricing of excess layers in P&C reinsurance is performed with well-known frequency and severity-based approaches using historical experience. For severity, it is a common practice to fit a single statistical distribution to historical claims. Fitting a single distribution to claims can be challenging when data is sparse or has outliers. This could lead to underestimating or overestimating claims especially at the tail end of distributions impacting pricing. In a competitive market, pricing anomalies can put reinsurers at a disadvantage against their competitors. Therefore, this article is aimed at showing how a piecewise Pareto distribution can be used for treaty pricing to overcome such difficulties in distribution fitting, leading to better outcomes for reinsurers. Traditional method of treaty pricing Generally, with treaty pricing claims are segregated into more frequent small claims, non-catastrophe large claims and catastrophe claims for their distinctive risk characteristics. Large claims such as large fire losses tend to be infrequent and have high severity. Claims over a selected threshold are considered as large claims and an appropriate statistical distribution is fitted to them. Then the fitted severity distribution and a claim frequency distribution, which comes from number of claims above the selected threshold, are aggregated to provide an aggregate claim distribution for pricing. This method is prevalent in the reinsurance market. We have observed that some reinsurers originating from Asia tend to use it. However, some well established large reinsurers coming from Europe and other parts of the world and even some medium sized reinsurers tend to use piecewise Pareto distribution for pricing potentially being motivated by the advantages Pareto distribution provides, which we discuss later and the straightforward mathematics [1] that can be used for pricing with piecewise Pareto distribution. Distribution fitting with the traditional method Underwriters and pricing actuaries typically use historical treaty experience to perform pricing. Historical individual claims are trended for inflation and adjusted for structural changes such as change in level of retention over time to reflect projected treaty period. Then distribution fitting is done on claims and a best fit is chosen using one or a selection of statistical criteria such as Least Squares Error, Kolmogorov or Anderson value. The outcome is a single fitted distribution. Difficulties with the traditional method This method of choosing one single distribution comes with its own drawbacks. If claims are not spread out reasonably well, for example, claims with a very few outliers, then distribution fitting becomes difficult. The difficulty stems from trying to fit a single distribution over a wider range often leading to overestimating or underestimating specifically at the tail end of the distribution. In some cases, we only get claims closer to the selected deductible leaving a wider range without any claims. This makes distribution fitting extremely difficult. A certain level of judgement is required with the help of risk profiles and market loss data to form a view on possible claims at the tail. The following graph illustrates the difficulty in distribution fitting with underestimated and overestimated areas in the fitted distribution. Pareto distribution and its popularity The Pareto distribution is named after the Italian civil engineer, Vilfredo Pareto, who came up with the concept of “Pareto efficiency”. The distribution is famously known as the Pareto principle or “80-20” rule. This rule states that, for example, 80% of the wealth of a society is held by 20% of its population. Social, scientific, actuarial and other fields widely use it. The Pareto distribution has two parameters, scale (or threshold) and shape (often denoted as alpha, α). The popularity and wide use of it in the actuarial field, especially with pricing can be attributed to several compelling reasons. Parameter invariance arguably is the most important feature, which implies that as long as we are in the tail the same alpha parameter applies whatever the threshold be [2]. The ease of deriving parameters using empirical data with techniques such as Method of Moment and Maximum Likelihood (MLE). Can be used to represent empirical data fairly well over a wide range of values. Availability of benchmarks for alpha values to help underwriters and actuaries to choose for pricing of different classes of business. Make it easier to explain parameter selections and results. Using one single Pareto distribution to fit can lead to issues mentioned previously. To work around these issues, the article introduces piecewise Pareto distribution. In fact, piecewise Pareto distribution is not new to actuarial practice. Underwriters and actuaries have been using it for a long time but its use has been limited in pricing. The next section of the article delves into treaty pricing with piecewise Pareto distribution. Pricing with piecewise Pareto distribution How this works is best explained with an example. Assume that we are pricing a non-proportional treaty layer with limit of $4 million in excess of $1 million deductible (i.e. 4m xs 1m) for treaty year 2018 having historical treaty results for the period 2010 to 2017. The basic idea of piecewise Pareto distribution is to split the layer being priced into chunks and fit separate Pareto distributions to them. First, we divide the layer limit into equal size chunks called priorities (You may split by a log scale as done in the given example). Second, we determine the number of claims exceeding each priority for each historical treaty year. (This is similar to assuming a large loss threshold and selecting number of claims above it for each treaty year to determine claim frequency with the traditional method). Then average exposure adjusted exceeding frequency for each priority is calculated with some weight assignment. In the example, two weight options have been given to choose from. For example, weight W1 gives equal weight to each historical treaty year whereas weight W2 discards the oldest treaty year giving equal weights to the rest of historical treaty years. The following table shows how the layer starting from the deductible of 1m to the end (i.e. limit + deductible) of 5m […]

In our June 2020 Bulletin number 002/ARB-BULLETIN/06/2020 we reviewed the quarterly financial performance of local professional reinsurance companies (IPR) for 2018 and 2019. Based on their latest published 1st Quarter 2020 results, this Bulletin attempts to further graphically depict the individual financial performance of IPR members, particularly in the wake of the Jakarta floods in early January 2020. In addition to the previous graphs covering: Solvency or RBC Level Investment Funds Equity Guarantee Funds or Assets. we have added two new graphs covering IPR members’ Profitability and Liquidity ratios (measured as Assets / Liabilities) : Solvency or RBC Level Based on OJK regulation the minimum RBC level for a local reinsurance company is 120%. All local reinsurance companies in the panel comply with this requirement   Investment Funds   Equity Based on OJK regulation No 67/POJK.05/2016 the minimum equity for a local reinsurance company is IDR 300 Billion All local reinsurance companies in the panel comply with this requirement   Guarantee Funds or Assets   5. Profitability   6. Liquidity If you have any issues on the above or on any other item please do not hesitate to contact: Bernard Krova – el.krova@arbrokers.asia Wayan Sumendra – wayan.sumendra@arbrokers.asia Adia Adithiya – adia.pradithama@arbrokers.asia To the extent this note expresses any opinion on any aspect of risk, the recipient acknowledges that any such assessment is an expression of PT Asia Reinsurance Brokers Indonesia’s opinion only, and is not a statement of fact. Any decision to rely on any such assessment of risk is entirely the responsibility of the recipient. PT Asia Reinsurance Brokers Indonesia will not in any event be responsible for any losses which may be incurred by any party as a result of any reliance placed on any such opinion.