Year loss table

Last updated

A year loss table (YLT) is a table that lists historical or simulated years, with financial losses for each year. [1] [2] [3] YLTs are widely used in catastrophe modeling as a way to record and communicate historical or simulated losses from catastrophes. The use of lists of years with historical or simulated financial losses is discussed in many references on catastrophe modelling and disaster risk management, [4] [5] [6] [7] [8] [9] but it is only more recently that the term YLT has been standardized. [1] [2] [3]

Contents

Overview

Year of interest

In a simulated YLT, each year of simulated loss is considered a possible loss outcome for a single year, defined as 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, due to the annual nature of many insurance contracts. [1]

Events

Many YLTs are event based; that is, 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.

Use in insurance

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

Examples of YLTs

YLTs are often stored in either long-form or short-form.

Long-form YLTs

In a long-form YLT, [1] each row 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.

YearEvent IDsEvent loss
1965$100,000
17$1,000,000
2432$400,000
3--
.........
100,0007$1,000,000
100,000300,001$2,000,000
100,0002$3,000,000

In this example:

Short-form YLTs

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 that year.

The same YLT above, condensed to a short form, would look like:

YearAnnual Total Loss
1$1,100,000
2$400,000
3$0
......
100,000$6,000,000

Frequency models

The most commonly used frequency model for the events in a YLT is the Poisson distribution with constant parameters. [6] An alternative frequency model is the mixed Poisson distribution, which allows for the temporal and spatial clustering of events. [10]

Stochastic parameter YLTs

When YLTs are generated from parametrized mathematical models, they may use the same parameter values in each year (fixed parameter YLTs), or different parameter values in each year (stochastic parameter YLTs). [3]

As an example, the annual frequency of hurricanes hitting the United States might be modelled as a Poisson distribution with an estimated mean of 1.67 hurricanes per year. The estimation uncertainty around the estimate of the mean might considered to be a gamma distribution. In a fixed parameter YLT, the number of hurricanes every year would be simulated using a Poisson distribution with a mean of 1.67 hurricanes per year, and the distribution of estimation uncertainty would be ignored. In a stochastic parameter YLT, the number of hurricanes in each year would be simulated by first simulating the mean number of hurricanes for that year from the gamma distribution, and then simulating the number of hurricanes itself from a Poisson distribution with the simulated mean.

In the fixed parameter YLT the mean of the Poisson distribution used to model the frequency of hurricanes, by year, would be:

YearPoisson mean
11.67
21.67
31.67
......
100,0001.67

In the stochastic parameter YLT the mean of the Poisson distribution used to model the frequency of hurricanes, by year, might be:

YearPoisson mean
11.70
21.62
31.81
......
100,0001.68

Adjusting YLTs and WYLTs

It is often of interest to adjust YLTs, perform sensitivity tests, or make adjustments for climate change. Adjustments can be made in several different ways. 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. [11]

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. [12] [13]

A general and principled method for applying weights to YLTs is importance sampling, [12] [3] in which the weight on the year is given by the ratio of the probability of year in the adjusted model to the probability of year in the unadjusted model. Importance sampling can be applied to both fixed parameter YLTs [12] 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 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, [12] in which years with high weights are repeated one or more times and years with low weights are deleted.

Calculating metrics from YLTs and WYLTs

Standard risk metrics can be calculated straightforwardly from YLTs and WYLTs. Some examples are: [1]

Related Research Articles

A parameter, generally, is any characteristic that can help in defining or classifying a particular system. That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

<span class="mw-page-title-main">Risk management</span> Identification, evaluation and control of risks

Risk management is the identification, evaluation, and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor, and control the probability or impact of unfortunate events or to maximize the realization of opportunities.

In the field of information retrieval, divergence from randomness, one of the first models, is one type of probabilistic model. It is basically used to test the amount of information carried in the documents. It is based on Harter's 2-Poisson indexing-model. The 2-Poisson model has a hypothesis that the level of the documents is related to a set of documents which contains words occur relatively greater than the rest of the documents. It is not a 'model', but a framework for weighting terms using probabilistic methods, and it has a special relationship for term weighting based on notion of eliteness.

Catastrophe modeling is the process of using computer-assisted calculations to estimate the losses that could be sustained due to a catastrophic event such as a hurricane or earthquake. Cat modeling is especially applicable to analyzing risks in the insurance industry and is at the confluence of actuarial science, engineering, meteorology, and seismology.

<span class="mw-page-title-main">Ensemble forecasting</span> Multiple simulation method for weather forecasting

Ensemble forecasting is a method used in or within numerical weather prediction. Instead of making a single forecast of the most likely weather, a set of forecasts is produced. This set of forecasts aims to give an indication of the range of possible future states of the atmosphere.

In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables.

Parametric insurance is a non-traditional insurance product that offers pre-specified payouts based upon a trigger event. Trigger events depend on the nature of the parametric policy and can include environmental triggers such as wind speed and rainfall measurements, business-related triggers such as foot traffic, and more. Examples of current parametric products include the Caribbean Catastrophe Risk Insurance Facility (CCRIF), the African Risk Capacity (ARC), and the protection of coral reefs in the state of Quintana Roo in Mexico.

<span class="mw-page-title-main">Catastrophe bond</span> Risk-linked securities

Catastrophe bonds are a subset of insurance-linked securities (ILS) that transfer a specified set of risks from a sponsor to investors. They were created and first used in the mid-1990s in the aftermath of Hurricane Andrew and the Northridge earthquake.

"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations which reflect the random variation in the input(s).

In statistics, overdispersion is the presence of greater variability in a data set than would be expected based on a given statistical model.

Loss reserving is the calculation of the required reserves for a tranche of insurance business, including outstanding claims reserves.

<span class="mw-page-title-main">Disaster risk reduction</span> Preventing and reducing disaster risk factors

Disaster risk reduction aims to make disasters less likely to happen. The approach, also called DRR or disaster risk management, also aims to make disasters less damaging when they do occur. DRR aims to make communities stronger and better prepared to handle disasters. In technical terms, it aims to make them more resilient or less vulnerable. When DRR is successful, it makes communities less the vulnerable because it mitigates the effects of disasters. This means DRR can make risky events fewer and less severe. Climate change can increase climate hazards. So development efforts often consider DRR and climate change adaptation together.

Complete spatial randomness (CSR) describes a point process whereby point events occur within a given study area in a completely random fashion. It is synonymous with a homogeneous spatial Poisson process. Such a process is modeled using only one parameter , i.e. the density of points within the defined area. The term complete spatial randomness is commonly used in Applied Statistics in the context of examining certain point patterns, whereas in most other statistical contexts it is referred to the concept of a spatial Poisson process.

<span class="mw-page-title-main">Hazard</span> Situation or object that can cause damage

A hazard is a potential source of harm. Substances, events, or circumstances can constitute hazards when their nature would potentially allow them to cause damage to health, life, property, or any other interest of value. The probability of that harm being realized in a specific incident, combined with the magnitude of potential harm, make up its risk. This term is often used synonymously in colloquial speech.

<span class="mw-page-title-main">Risk</span> Possibility of something bad happening

In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value, often focusing on negative, undesirable consequences. Many different definitions have been proposed. One international standard definition of risk is the "effect of uncertainty on objectives".

In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent zero-valued observations.

<span class="mw-page-title-main">Poisson point process</span> Type of random mathematical object

In probability theory, statistics and related fields, a Poisson point process is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The process's name derives from the fact that the distribution of the number of points regions of the same size has a Poisson distribution. The process and the distribution are named after French mathematician Siméon Denis Poisson. The process itself was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and actuarial science.

Caribbean Catastrophe Risk Insurance Facility Segregated Portfolio Company is an insurance company headquartered in the Cayman Islands. The sixteen original member-countries of CCRIF included participants in CARICOM, and the membership of the Board of Directors is selected by CARICOM and by the Caribbean Development Bank.

<span class="mw-page-title-main">Howard Kunreuther</span> American risk analyst (1938–2023)

Howard Charles Kunreuther was an American economist. He was the James G. Dinan professor emeritus of decision sciences and public policy at the Wharton School of the University of Pennsylvania.

References

  1. 1 2 3 4 5 6 Jones, M; Mitchell-Wallace, K; Foote, M; Hillier, J (2017). "Fundamentals". In Mitchell-Wallace, K; Jones, M; Hillier, J; Foote, M (eds.). Natural Catastrophe Risk Management and Modelling. Wiley. p. 36. doi:10.1002/9781118906057. ISBN   9781118906057.
  2. 1 2 3 Yiptong, A; Michel, G (2018). "Portfolio Optimisation using Catastrophe Model Results". In Michel, G (ed.). Risk Modelling for Hazards and Disasters. Elsevier. p. 249.
  3. 1 2 3 4 5 6 Jewson, S. (2022). "Application of Uncertain Hurricane Climate Change Projections to Catastrophe Risk Models". Stochastic Environmental Research and Risk Assessment. 36 (10): 3355–3375. Bibcode:2022SERRA..36.3355J. doi:10.1007/s00477-022-02198-y. S2CID   247623520.
  4. 1 2 Friedman, D. (1972). "Insurance and the Natural Hazards". ASTIN. 7: 4–58. doi: 10.1017/S0515036100005699 . S2CID   156431336.
  5. 1 2 Friedman, D. (1975). Computer Simulation in Natural Hazard Assessment. University of Colorado.
  6. 1 2 3 Clark, K. (1986). "A Formal Approach to Catastrophe Risk Assessment and Management". Proceedings of the American Casualty Actuarial Society. 73 (2).
  7. ↑ Woo, G. (2011). Calculating Catastrophe. Imperial College Press. p. 127.
  8. ↑ Edwards, T; Challenor, P (2013). "Risk and Uncertainty in Hydrometeorological Hazards". In Rougier, J; Sparks, S; Hill, L (eds.). Risk and Uncertainty Assessment for Natural Hazards. Cambridge. p. 120.
  9. ↑ Simmons, D (2017). "Qualitative and Quantitative Approaches to Risk Assessment". In Poljansek, K; Ferrer, M; De Groeve, T; Clark, I (eds.). Science for Disaster Risk Management. European Commission. p. 54.
  10. ↑ Khare, S.; Bonazzi, A.; Mitas, C.; Jewson, S. (2015). "Modelling Clustering of Natural Hazard Phenomena and the Effect on Re/insurance Loss Perspectives". Natural Hazards and Earth System Sciences. 15 (6): 1357–1370. Bibcode:2015NHESS..15.1357K. doi: 10.5194/nhess-15-1357-2015 .
  11. ↑ Jewson, S. (2023). "A new simulation algorithm for more precise estimates of change in catastrophe risk models, with application to hurricanes and climate change". Stochastic Environmental Research and Risk Assessment. 37 (7): 2631–2650. Bibcode:2023SERRA..37.2631J. doi:10.1007/s00477-023-02409-0.
  12. 1 2 3 4 Jewson, S.; Barnes, C.; Cusack, S.; Bellone, E. (2019). "Adjusting Catastrophe Model Ensembles using Importance Sampling, with Application to Damage Estimation for Varying Levels of Hurricane Activity". Meteorological Applications. 27. doi: 10.1002/met.1839 . S2CID   202765343.
  13. ↑ Sassi, M.; et al. (2019). "Impact of Climate Change on European Winter and Summer Flood Losses". Advances in Water Resources. 129: 165–177. Bibcode:2019AdWR..129..165S. doi:10.1016/j.advwatres.2019.05.014. hdl: 10852/74923 . S2CID   182595162.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.