Year loss table

In a simulated YLT, each year of simulated loss is considered a possible loss outcome for a single year, the year of interest, which is usually in the future. In insurance industry catastrophe modelling, the year of interest is often this year or next year, due to the annual nature of many insurance contracts.[1] However, the year can also be defined to be any year in the past or the future.

Many YLTs are event based i.e., they are constructed from historical or simulated catastrophe events, each of which has an associated loss. Each event is allocated to one or more years in the YLT and there may be multiple events in a year.[4][5][6] The events may have an associated frequency model, that specifies the distribution for the number of different types of events per year, and an associated severity distribution, that specifies the distribution of loss for each event.

Events in an event-based YLT may all be of one peril-type (such as hurricane) or may be a mixture of peril-types (such as hurricane and earthquake).

YLTs represent the possible losses in a period of one year, but can be generalized to represent the possible losses in any length of time, in which case they may be referred to as Period Loss Tables (PLTs).

YLTs are widely used in the insurance industry,[1][2] because they are a flexible way to store samples from a distribution of possible losses. Two properties, in particular, make them useful:

• The number of events within a year can be distributed according to any probability distribution, and is not restricted to the Poisson distribution
• Two YLTs, each with ${\displaystyle N}$ years, can be combined, year by year, to create a new YLT, also with ${\displaystyle N}$ years.

In a long-form YLT,[1] each row of the YLT corresponds to a different loss-causing event. For each event, the YLT records the year, the event, the loss, and any other relevant information about the event.

In this example:

• The Events IDs refer to a separate database which defines the characteristics of the events, known as an event loss table (ELT)
• Year 1 contains two events: events 965 and 7, with losses of $100,000 and $1,000,000, giving a total loss in year 1 of $1,100,000
• Year 2 only contains one event
• Year 3 contains no events
• Event 7 occurs (at least) twice, in years 1 and 100,000
• Year 100,000 contains 3 events, with total loss of $6,000,000

In a short-form YLT,[3] each row of the YLT corresponds to a different year. For each event, the YLT records the year, the loss, and any other relevant information about the year.

The same YLT as above, but condensed to short-form, would look like:

The most commonly used frequency model for the events in a YLT is Poisson distribution with constant parameters.[6]

An alternative frequency model is the mixed Poisson distribution, which allows for temporal and spatial clustering of events.[10]

If a YLT has been created by simulating from a list of events with given frequencies, then one simple way to adjust the YLT is to resimulate but with different frequencies.

Resimulation with different frequencies can be made much more accurate by using the incremental simulation approach.[12]

YLTs can be adjusted by applying weights to the years, which converts a YLT to a WYLT. An example would be adjusting weather and climate risk YLTs to account for the effects of climate variability and change.[11][13] By putting more weights on some years and less on others, the implied distribution of events changes, and the distributions of event loss and annual loss change accordingly.

Adjusting an existing YLT to represent a different view of risk, as opposed to rebuilding the YLT from scratch, may have the benefit that it avoids having to resimulate the events, the positions of the events in the years, and the losses for each event and each year. This may be more efficient.

One general and principled method for applying weights to YLTs is importance sampling[11][3] in which the weight on the year ${\displaystyle i}$ is given by the ratio of the probability of year ${\displaystyle i}$ in the adjusted model to the probability of year ${\displaystyle i}$ in the unadjusted model. Importance sampling can be applied to both fixed parameter YLTs[11] and stochastic parameter YLTs.[3]

WYLTs are less flexible, in some ways, than YLTs. For instance, two WYLTs, with different weights, cannot easily be combined to create a single new WYLT. For this reason, it may be useful to convert WYLTs to YLTs. This can be done using the method of repeat-and-delete,[11] in which years with high weights are repeated one or more times, and years with low weights are deleted.