Marine insurance: Model ships
Marine insurance is the oldest class of insurance business in the world. In spite of its long history, premium rating techniques for this class are relatively unsophisticated. Steps have been taken in recent years to develop technical underwriting tools, but progress has been limited. Underwriters typically have access to vessel rating tables, but the origin of these tables is often uncertain and rating tables are likely to be based more upon general intuition than upon rigorous statistical analysis.
In a paper presented to the International Union of Marine Insurance (IUMI) in September 2005, Rolf Tolle, franchise performance director at Lloyd's, emphasised the importance of “applying performance management to marine business”. In particular, he made the case for a robust system for pricing. However, the supply of suitable historic loss data and/or models to provide the foundations of such a system is rather limited.
In an attempt to contribute to the development of a more scientific approach to marine hull pricing in particular, we are developing a series of market loss frequency models using modern actuarial techniques. We don’t expect statistical models to render marine underwriters’ experience and intuition obsolete, and nor should they, but we do believe that robust statistical analysis of market data has a lot to offer.
We decided to investigate the influence that a number of risk factors have had on market experience, using the statistical technique of generalised linear modelling (GLM) applied to a large extract describing market losses. GLMs came into common usage by non-life actuaries in the early 1990s and are now very widely used in the creation of rating models. We are not currently aware, however, that marine hull market loss experience has been widely modelled in this way.
It would be possible to analyse loss frequency using simple tables showing how it varies with respect to vessel age, gross tonnage, and so on. Although this would be useful, the GLM approach is better in two crucial ways. First, it helps us to estimate the true effect of each risk factor, all else being equal, in a way that more simple analyses cannot. Second, it helps us to distinguish genuine trends from random fluctuations in experience.
The data extract underlying the analysis has two components, joined together for modelling purposes. First, we obtained a list of known market losses occurring between 1 January 1990 and 31 December 2006. Second, we obtained a corresponding set of exposure data – a snapshot of the world’s shipping fleet of vessels of 100 gross tons or more as at each 31 December from 1990 to 2006 inclusive.
Initial Results
We have used the GLM approach to look at the influence of a large number of risk factors, including vessel age, type and tonnage, on loss experience. Some results of this analysis are presented here. As an example, Figure 1 shows the relative loss frequency for the marine hull class by age of vessel across all types of loss.
There is a general upward trend in loss frequency with respect to age until vessels are around 20 years old, with frequency declining slowly thereafter. This may be a result of changes in the vessels' physical condition, cargo type, type of and number of voyages as they age. Figure 2 shows how the loss frequency varies with gross tonnage. Again, historically there is a general upward trend in loss frequency – larger, heavier vessels tend to be involved in more accidents.
Our final example, Figure 3, shows the changes in loss frequency over time. There is some variation from year to year as a result of random fluctuations. We do, however, see a general downward trend in loss frequency during the 1990s, although this seems not to have continued into the current decade. Various factors may have influenced experience here – the 1991 Gulf War, changes in economic activity and trade volumes caused by the 1998 Asian financial crisis, 9/11, and so on. This information is of course retrospective and not directly applicable to a prospective rating model, but underwriters may at least be able to take a view about recent loss frequency trends and ensure that any rating structure they produce reflects this view.
The next step
The analysis presented here is at an early stage and more detailed modelling will follow. In particular, the initial model considers all loss types together, but we will create separate models for the various primary causes of loss, such as collision or fire, and for each severity indicator such as total loss or serious loss. They are likely to be more robust and, crucially, help us to interpret why certain patterns occur in the data in a more intuitive way. We will release details of our subsequent findings as they emerge, and I would also be interested in hearing the views of interested parties on the interpretation and deployment of these models.
Dmitri Subotsky works for JLT Reinsurance Brokers
Figure 1 Key (see below)
>> Yellow bars – Distribution of exposure (in ‘ship years’) by age
>> Green line – Influence of the vessel age on relative loss frequency (absolute frequencies are not shown in these graphs since they depend not only upon age but also upon the other factors listed above as well as many others), relative to a notional ‘base’ category which, in this instance, is the ‘36+’ band
>> Blue lines – Approximate 95% ‘confidence interval’, in recognition of uncertainty in all of these estimated relative frequencies due to random variations in the data. The data extract is large, however, and as a result the uncertainty around our estimates is fairly small.
Dmitri Subotsky
