How Does Liability Risk Modeling Work? Insight into the Foresight
RJ Briggs | August 1, 2018
This article originally appeared in The Risk Report, which provides analysis and interpretation of the latest innovations in insurance coverage and discussions of risk management best practices. Learn more about subscribing to The Risk Report here.
Footnotes
1 Borel v. Fibreboard Paper Products Corp., 493 F.2d 1076 (5th Cir. 1973), was filed in 1969.
2 Beyond these basic modules, proprietary software typically contains one further component that allows insurers to examine the impact of different policy terms on potential losses. This layer of the software generates actionable information for underwriting, enterprise risk management, and underwriting strategy. When insurers have strong confidence over how policy terms will be interpreted in practice, these layers can be highly specific and tightly implemented.
3 Practitioners may reasonably disagree with the module boundaries set forth in this article. The decomposition used here is simply intended to aid exposition.
4 See also Towers Watson (2011) for more information.
5 With respect to legal doctrine, for example, consider liability for climate change. Science has largely settled on the anthropogenic nature of climate change, but the tort system would have to change substantially to allow for injured parties to successfully sue for related damages (Kysar, 2011). As to commercial activity, consider induced seismicity. While science established the connection between wastewater injection and the risk of induced seismicity 50 years ago , it was the recent doubling of injection rates in Oklahoma combined with a previously unknown geologic suitability that led to an increase in earthquake risk in the state (Rubinstein and Mahani, 2015).
6 Although property damage from pollution is typically excluded from commercial general liability and excess casualty policies except on a sudden and accidental basis, products liability can nonetheless extend to property damage as in asbestos and MTBE litigation (among others).
7 Many catastrophic scenarios (e.g., Ruffle, et al., 2014) have influence beyond liability covers. For these kinds of events, it is common to aggregate results at the line-of-business level as well.
8 Treaty reinsurance bordereaux typically reveal only the industry classifications of transferred risks rather than company specific information, so industry aggregate results are informative here.
9 See Hall et al. (2012) for an introduction to relevant methods.
10 For occurrence form commercial general liability policies, the judicial application of policy terms to determine which policy years would respond to the loss presents a further dimension of uncertainty. These rules vary by jurisdiction and over time. Because the existing literature does not roundly address this aspect of the problem, I subsume it into the assignment of losses across years, generally. Reville and Boudreau (2017) and Sclafane (2017) discuss occurrence form uncertainty from the perspective of Praedicat but do not delve into model details.
11 As a point of reference, D'Arcy (2016) fits a gamma distribution to the Towers Watson (2011) data. For reserving purposes, this approach suggests "using $107 billion for a 1 in 100 year event and $141 billion for a 1 in 250 year event is a reasonable place to start."
Abstract
Liability catastrophe risks are present in every major insurance and reinsurance portfolio, but they remain poorly measured. A variety of solutions have begun to address this problem. This article assesses the progress made, comparing and contrasting the various approaches as much as the published details allow. It provides context for considering the current state of liability catastrophe modeling and how it can move toward creating an accepted set of standards and benchmarks for regulatory and rating purposes. The closing discussion considers the overall state of liability catastrophe modeling today and provides ideas for how the field can mature.
The specter of liability catastrophe, alternatively referred to as casualty catastrophe, haunts the portfolios of insurers and reinsurers across the industry, from smaller regional concerns to the largest companies in the market. These events, defined as large ($100 million or greater), correlated losses that evolve over time, have a reputation as black swans: difficult to predict, one-of-a-kind events that can emerge suddenly and have massive impacts on many years' worth of commercial general liability and excess casualty polices.
Asbestos litigation remains the quintessential example. Nearing its sixth decade and topping $100 billion in losses (A.M. Best, 2017), defendants in this litigation come from dozens of divergent industries.1 Towers Watson (2014) lists more than 40 past and possible future liability catastrophes, including litigation surrounding lead paint, methyl tertiary-butyl ether (MTBE), Bisphenol A, and climate change. With the pace of technological development arguably accelerating, and regulatory regimes always trying to catch up, the list of potentially hazardous products and their uses only continues to grow.
Over the last several years, a variety of solutions have begun to address the notoriously thorny modeling problem these events present. While much of the work in this field remains proprietary, the structure of these models are sketched in a variety of white papers and presentations published in the field by leaders such as AIR Worldwide (formerly as Arium), Cambridge Centre for Risk Studies, Guy Carpenter, Lloyd's of London, Praedicat, Swiss Re, and Willis Towers Watson (formerly as Willis Re and Towers Watson, separately). At their core, the approaches that each of these sources outlines harness the familiar and well-developed natural catastrophe modeling framework that came into practice nearly 30 years ago, revolving around the analysis of appropriate scenarios and event sets. As the available corpus points out, liability risk accumulation measurement demands extensions to the natural catastrophe paradigm. The published details present a variety of solutions, each with their advantages and drawbacks.
Precisely how are liability catastrophe models built: what kind of foresight do they offer, based on which assumptions and data? To answer these questions, it's important to break the liability catastrophe problem into component modules and then compare and contrast the published material on each. Doing so unifies much of the existing literature, highlighting where models have made the most progress and where the biggest challenges remain.
The literature on liability catastrophe models remains sparse and short on detail. D'Arcy (2016) offers perhaps the best review to date, providing background on the problem, working through several examples to build intuition, and offering insight into the way ratings agencies and regulators presently address liability catastrophe risk. Relative to D'Arcy, this paper presumes the reader is more familiar with liability catastrophes, delves more into the models themselves, and provides an update based on materials recently published.
In brief, adapting the natural catastrophe lens decomposes the problem into a set of four familiar modules: hazard, inventory, vulnerability, and loss. Most models rely on expert opinion to identify hazards, and few appear to provide a model for their unconditional frequency. Practitioners roundly agree that risk mapping pertains to industries, but they differ in how to measure exposure within an industry and how to understand risk correlations across industries. Generally, loss models take either a "top-down" or a "ground-up" approach, working from loss data or models of underlying generative processes, respectively. However, both approaches can learn from the other. While liability modeling has made significant advances, the industry has not converged on a standard paradigm. Indeed, observers cannot presently compare models on a common, objective basis.
This article begins with an overview of the structure of natural catastrophe models. This framework is then applied to liability catastrophes, examining each module in turn. I focus on the main problems for liability modelers, review published solutions, and offer questions for model developers and users to consider as progress in this area continues. Finally, the market for these models is discussed, and suggestions for how market participants might work to establish model credibility and comparability to support the development of benchmarks and standards are offered.
Natural Catastrophes Models
Since catastrophes are rare events, modelers typically have little historical data to work with that directly captures the phenomenon of interest. They, therefore, proceed by building stochastic models that describe how a catastrophe might arise through the combination of rare circumstances, with elements of the model driven by better understood, data-rich phenomena. Running this model many times (i.e., applying Monte Carlo methods) reveal a set of outcomes—an "event set"—where catastrophes occur at some frequency.
Because of the relative familiarity and success of the paradigm, most discussions of liability risk modeling start by using natural catastrophe models as an imperfect analogy (e.g., Towers Watson: Ball and Cohen, 2014; Lloyd's and Praedicat Inc., 2015; and Marsh, 2018). Grossi and Kunreuther (2005) provide the textbook description of these models. In their formulation, standard natural catastrophe models are composed of four basic modules: hazard, inventory, vulnerability, and loss.
The hazard module is the primary engine of a catastrophe model. It provides a probabilistic description of the underlying risk that ultimately generates loss. Hurricane modeling today, for example, applies meteorological science to estimate parametric relationships between input variables like ocean temperatures and weather events to create near-term forecasts of the risk (e.g., AIR Worldwide, 2015). Such models may have several components. Work published by authors affiliated with Risk Management Solutions (RMS), for example, combines modeled distributions of hurricane genesis, translational speed and heading, central pressure over water, inland filling rates, maximum velocity, and maximum radii (Bonazzi, et al., 2014). Forecast changes in the input variables in these models then drive forecasts of hurricane risk.
The set of property that can be affected by a hazard is referred to as the inventory. Elements of this set have characteristics that influence how they respond to different realizations of the hazard, such as location, building construction details, age, and so on. While some elements of an inventory could be generated in part by a stochastic model, traditionally this set is known with relative confidence in property catastrophe applications. Particularly with the advent of commercial satellite mapping, property insurers can often access abundant information relevant to understanding risk exposures.
The vulnerability module combines realizations of the hazard module with the inventory to estimate the physical damage different events would do to properties. Staying with the hurricane risk example, vulnerability takes geocoded information from an event generated by the hazard module like storm track, wind speeds, and storm surge. These event characteristics can then be mapped to properties in the inventory, with different estimated physical damage to the properties based on property characteristics: newer construction with less exposure to wind shear, for example, may weather the storm better.
Finally, the loss module translates physical damage into estimated dollar amounts for direct losses for the repair or replacement of property. Indirect costs for business interruption or temporary relocation may also be estimated if appropriate to the policy. Again, this model is typically stochastic to account for any uncertainties. For the hurricane example, output from this module would include estimated loss curves—frequency and severity of loss—for each element of the inventory.2
Liability Catastrophe Modeling: What's Different?
In this section, I step through the liability catastrophe problem through the lens of the four natural catastrophe modules and point out the new problems that arise.3 Generally, modelers in this area agree that three recurring themes explain most of the differences: the socio-technological context of liability risk, the long timelines over which liability catastrophes can unfold, and the nature of third-party cover versus first-party cover (cf. D'Arcy, 2016; Lloyd's and Praedicat, 2015; and Lloyd's and Arium, 2016). Where information exists, some of the proposed solutions to date are discussed.
Liability Hazard Identification and Frequency
The natural catastrophe modeling paradigm immediately runs into a problem when applied to liability risks: the hazards themselves are not well known. Millennia of human experience and recorded history attest to the risks of earthquakes, fires, floods, hurricanes, landslides, tornadoes, tsunamis, and volcanic explosions. Scientific advances over the last few centuries have vastly improved our ability to understand these events. While the earth's changing climate and other factors may pose new complications for modelers in this domain, there is really nothing new under the sun.
Liability risk modeling, therefore, starts one step back, beginning with identification of the risks. Insurers typically have emerging risk committees to serve this function, and brokers or scenario vendors may similarly determine which risks merit analysis (e.g., Guy Carpenter, September 2014; and Willis Re, 2014). While widely adopted and flexible over the types of risks that can be considered, this approach lacks clear and consistent criteria for identification. Coupled with an ever-shifting socio-technological landscape, modelers using this approach have little assurance that they are considering the full catalog of the most important risks, and they have no objective basis to rate the relative likelihood of those risks.
The emerging risk committee method predominates because, as Guy Carpenter (December 4, 2014) notes, "modeling technology … tends to be exasperated by the lack of available essential data." Because each casualty catastrophe is unique and unrepeatable, modelers cannot rely exclusively on claims history for information on potential risks in the future. Towers Watson (2014) nonetheless argues that the "features of historical casualty catastrophes yields clues about the characteristics of the next industry changing event."4 Cambridge Centre for Risk Studies (2017) embraces a similar idea for identification, arguing for scenario development based on a threat taxonomy of potential causes of loss generated by reverse engineering historical precedents or other scenarios.
Towers Watson (2014) carries the idea into a structural model. Sampling from a proprietary database of more than 300 casualty catastrophes and their characteristics, they create an event set with permutations of the characteristics that can be analyzed against the reference set. This approach remains somewhat constrained by historical data and is silent on what actual developments may lead to the new events described. Nonetheless, it does offer an expanded view of what could happen and allows users to see how distinct factors could unexpectedly come together to create a catastrophe.
While wholly distinct in other ways, Lloyd's and Arium (2017) describe a kindred methodology that relies on proprietary categorizations of liability events found in Advisen's (2015) loss data in terms of the "shapes" of economic relationships among affected parties. Historical data then play a role in providing the basis for simulating losses for events described by experts using the shapes framework: "These shapes are used to create a large catalogue of scenarios, including potential mega-liability events that exceed asbestos." While the methodology still relies on experts to identify emerging risk scenarios to model and does not appear to have an objective measure for their unconditional likelihood, it does generate event sets for each scenario that can be analyzed in terms of frequency and severity.
Alternatively, Lloyd's and Praedicat (2015) argue that the spectrum of risks can be revealed by using data mining to "identify bodily injury and environmental property damage hypotheses in the scientific literature." According to this view, biomedical science can identify risks for liability insurers because U.S. courts treat scientific evidence in a predictable fashion, per the standard established in Daubert v. Merrell Dow Pharmaceuticals, 509 U.S. 579 (1993). Praedicat then uses metrics from data mining to "generate predictions for the trajectory of the science … and estimate the risk of future litigation in each setting." While this method provides an objective lens for hazard identification and frequency modeling, it is not clear whether it is wholly sufficient. Risks driven by developments outside of science, such as shifts in legal doctrine or changes in commercial activity patterns, may not be covered.5 Science is also not necessary to establish damage to property: the unwanted presence of a substance, even an innocuous one, can be enough.6
Swiss Re (2016) offers another forward-looking, structural approach built around scenarios. The Liability Risk Drivers (LRD) model allows the probability of each hazard to depend on distinct factors. These factors, which are observable and external to the risk itself, are then structurally modeled and projected over each legal environment of interest. While the details of this approach are not entirely clear from published materials, Swiss Re (2017) discusses how it applies to product liability risk as a category of scenarios. In the framework, product liability risks are modeled as dependent on three overarching factors by region: the emergence of new products, the propensity to sue, and the likelihood of mass litigation. In turn, these factors depend on observable covariates. For example, the emergence of new products might depend on the type of products considered, the geographic spread of those products, and economic factors.
Overall, the solutions to hazard identification and frequency modeling to date raise at least two questions. First, is the systematic identification of liability catastrophe hazards necessary, or is it sufficient to build a broad library of scenarios that responds to risks after they have emerged? Most of the models presented to date continue to rely on expert judgment for identification, implicitly adopting the idea that the long latency of liability catastrophes affords market participants time to see risks taking shape. The systematic, science-driven approach described in Lloyd's and Praedicat (2015) may offer earlier indications for a significant subset of liability risks, though some risks lie beyond its reach. The genetic approach of Towers Watson (2014) has the advantage of generating novel hazards that would not have otherwise been considered, but users need to consider the plausibility of scenarios generated by this approach as they do not necessarily connect to current trends.
Second, given a set of risks to monitor, how informative are frequency data on past catastrophes for understanding the likelihood of future catastrophes? Notably, none of the models presented here appear to rely on historical frequency to project future hazard likelihood, although loss data see use in other ways. The models outlined in Towers Watson (2014) and Lloyd's and Arium (2017) principally rely on historical data to estimate frequency, severity, and correlation structure by industry, conditional on an event occurring, but they do not appear to give unconditional probabilities of the risks themselves. Praedicat and Swiss Re's models rely on other data sets to generate likelihood information, but their underlying theories remain to be tested in some open, verifiable sense.
Liability Inventory: Companies, Industries, and Vulnerability
In liability catastrophes, insurance losses are ultimately generated by companies with liability for bodily injury or damage to property. We can, therefore, think of the inventory of liability catastrophe models as a set of companies and covariates that drive their vulnerability to liability catastrophe risks. In this setting, vulnerability can be thought of as a function that describes the share of claims that would accrue to each of the companies in the inventory given a realization of the hazard. For each hazard, then, modelers must determine which covariates drive relative liability and how they do so.
In aggregate, losses accrue to industries and, for the purposes of reinsurance, to insurers.(Footnotes 7, 8 Most of the published material that this paper reviews discusses models and results in terms of these aggregate levels. But for liability models to be actionable for underwriting strategy and insurance enterprise risk management, company-level results are necessary. Methods and results at this level are proprietary because of their value, but the published material nonetheless does reveal some of the core ideas.
Generically, model designers rely on industrial classifications and company revenue to capture company vulnerability in their models. For example, in Swiss Re's (2016) "risk splitter" module of its LRD model, the "allocation of business volume to the different incoming scenario loss models [is] according to the exposure split by location per type of product/activity," and "the frequency of the potential losses is determined by the risk driver 'size of company; and some loss scenario properties.'" Lloyd's and Arium (2017) similarly relies on industry classifications, developing parameterized shapes among them, and company size to allocate losses within industries.
This approach works with the information insurers and reinsurers typically have across their books of business, but it runs into a few problems. First, industrial classifications can be very broad and are not necessarily reflective of exposure to a given risk. As Kipperman (2016) points out:
By way of analogy to property catastrophe, industrial classification information would be similar to a hurricane catastrophe model inventory that labels property as "coastal." While such information has value, it could be much more precise.
Accepting the imperfect mapping between a company's industrial classifications and its risk exposures, the question then becomes how to use the information to measure relative liability risk and account for potential correlation in losses. Two modelers in the area discuss their solutions. Lloyd's and Arium (2017) make use of "the economic relationships in the supply chains" among industries, arguing that these shapes trace out the "fault lines of economic liability." In effect, the idea is that if a supplier manufactures something hazardous, downstream industries with a greater dependence on the supplier will have a greater exposure to the hazardous product. The relative size of trade flows can, therefore, inform sampling weights for loss allocation at the industry level. While this model does not solve the conflation between industry and risk, it relies on externally valid data relevant to the problem, eliminates correlation among industries that do not do business together, and provides a useful baseline.
Praedicat (2017) identifies industry and company risk exposure separately by bringing company-level data to the problem. In-house experts "map and characterize … potential litigation by groups of lawsuits," with attention to "exposure setting, and set of defendant types" (i.e., industries). At the same time, "analysts and algorithmic methods connect companies to these industries." Combining this information and other sources, they report that their "loss allocation model generates loss share distributions at the industry and company level." Per this source, loss shares in this model are driven by the following three factors.
Although this approach brings a finer level of detail to the problem, it raises at least two issues. First, with respect to data derived from expert judgments and algorithmic methods, the underlying data wants for external validation by users: "garbage in, garbage out" is otherwise possible. Second, even in this simplified description, this model sounds somewhat involved. Liability modeling is inherently complex because of its subject; but, as model complexity increases, the curse of dimensionality takes hold, and model uncertainty increases exponentially. Model users may want to understand the sensitivity of results to key structural and parametric assumptions to improve decision-making.9
Returning to the use of revenue as a covariate of liability risk, it is an open question whether "bigger" means more likely to be held liable. As Macoun (1996) explains:
Both Vidmar (1993) and MacCoun (1996) fail to find support for the "deep pockets" hypothesis, in medical malpractice and personal injury cases, respectively. Contrariwise, Lloyd's and Arium (2017) believe that:
This result has at least two explanations: either the deep-pocket hypothesis is correct for products liability, or large companies in the loss data also tended to have a true, greater share of the underlying risk. Praedicat (2017) attempts to measure exposure to underlying risk by estimating "industry market share" for each company and industry, but empirically it is not clear which approach better explains the data.
Damage and Losses: What and When?
The loss module of a liability catastrophe model is similar to the natural catastrophe model in that it combines a realization of the hazard with information about elements of the inventory to generate estimated losses before the application of policy terms. In liability modeling, "damages" are lawsuits and associated costs for defense and indemnity rather than costs for destroyed buildings. Liability models must also contend with the temporal dimension. Except for sudden, idiosyncratic events, such as explosions or isolated product failures (e.g., Takata airbags), liability catastrophes unfold over time, potentially spanning decades and affecting many years of business.10 Understanding the time path of potential liability is critical—because of the time value of money, losses expected further out in the future require less reserve capital today.
With respect to the loss module, modelers generally take one of two approaches to the problem. On one side, the "top-down" approach essentially argues that historical losses put in appropriate context with other covariates and intelligently sampled can provide useful insight into potential future losses. Towers Watson (2011) describes a model like this, saying in part:
Lloyd's and Arium (2017) likewise draw on historical loss distributions, noting that distributions for economic parameters, including the size of loss and period of time over which losses arise, "are often fitted to historical data and adjusted for expert input."11
Other modelers eschew past losses as largely uninformative on the size of future risks and build prospective severity models using a wide variety of input data sets. These models work from first principles on disease rates, costs of specific injuries, wages, and more. Cambridge Centre for Risk Studies (Coburn, 2017) argues for this kind of "ground-up" modeling, noting:
Such models typically have many different interacting components. Swiss Re (2016), for example, describes the "price tag engine" of their LRD model as follows:
Praedicat (2017) similarly describes a ground-up model for bodily injury losses, with severity over time as a function of the number of individuals estimated exposed, the fraction of those likely to be injured, cost of the injury, latency of the disease, the strength of the plaintiff's case, and the cost of negotiating settlements.
Overall, the divide between top-down and ground-up modeling reduces to assumptions on process stability. Implicitly, top-down models assume some critical parts of the generative process for these events remain stable over time so that the adjusted loss distribution continues to be informative and the model stays as simple as possible. The ground-up approach rejects the idea that the historic loss distribution is informative because of the rarity of the phenomenon of interest and the unique circumstances of each historical event. Instead, it attempts to identify and model the contributing processes explicitly to generate loss estimates at the price of added model complexity. In spite of their philosophical difference, each of these approaches can learn from the other. Top-down modelers can explore ground-up models for insights on dynamic processes important to capture in data adjustments, while ground-up practitioners can make use of loss history data and near-misses to benchmark and parameterize their models.
Fulfilling the Promise of Liability Risk Modeling
Natural catastrophe modeling has transformed property insurance and vastly expanded opportunities for risk transfer and management. Liability catastrophe modeling holds similar opportunities, and many in the field argue that its time has arrived. Swiss Re (2016), for example, states that "the LRD approach enables us to improve risk selection and generates a competitive advantage for both Swiss Re and our strategic clients." AIR Worldwide (2018) likewise trumpets, "Finally, casualty insurers can benefit from modeling risk, just as property insurers have for the past 30 years." Praedicat (2018) goes further still, claiming that its models now provide sufficient granularity for insurers to create new products that underwrite specific, "named peril" liability risks that standard forms would otherwise exclude. Objectively, it is an open question whether the models can actually deliver on these promises.
Although the publications reviewed here provide some insight into the approaches that modelers use, the lack of detail precludes the open assessment of methodologies that would allow regulators or rating agencies to identify and endorse standards for liability catastrophe models as they have for natural catastrophe models. Such standards would significantly benefit the market and drive their adoption. In his review, D'Arcy (2016) concludes that, in spite of all the recent progress in the field, much remains to be done, noting that:
Appropriate incentives combined with better data on past liability catastrophes, D'Arcy argues, are necessary for model improvements.
While private market incentives presently appear strong enough to drive further improvements, the call for more data begs the question: what data are relevant for understanding liability catastrophes? The models discussed in this article have wide disparities, with fundamentally different philosophies on the underlying generative processes of liability risk, the value of historic loss data, and the role of expert opinion. They differ even on the sets of hazards they identify. While liability modeling does not easily lend itself to the same kind of peer-reviewed, scientific research and publication available to natural catastrophe modelers, market participants nonetheless could open their methods to more scrutiny and facilitate comparisons.
One means to do so would be to publish retrospective applications of models to some set of prior catastrophes. For example, how do today's models explain asbestos litigation? When would they have raised the alarm, how much loss would they have estimated, and what would be the expected allocation of losses over industries and time? With the wealth of information available to the industry on asbestos losses and the detailed research on costs and causes of the litigation (e.g., Carroll, et al., 2005), this kind of effort seems both feasible and valuable.
To foster comparability over present risks, stakeholders in the industry could begin by establishing a reference set of hazards for all liability catastrophe models to address. Modelers might publish periodic metrics on this set of risks so that observers could compare their results over time and match projections to eventual reality. Participants could create synthetic reference portfolios for testing models and benchmarking results to facilitate this effort. Lessons learned in the process of creating the schema for reference portfolios could have the side benefit of improving risk transfer across the industry by reducing frictions in the exchange of information.
At least one collaborative data effort in the industry is already underway. Taking into account the importance of interoperable data as well as the diversity of views on what data matter, Cambridge Centre for Risk Studies and RMS (2018) are leading the Global Exposure Accumulation and Clash Project, which aims to create a multiline insurance exposure data schema. The project has several goals, including "[providing] a more comprehensive and standardized framework for monitoring and reporting exposure" and "[enabling] a new generation of models and risk analytics as well as [expanding] the scope of potential risk management applications." The project consults with industry stakeholders across the spectrum and is presently nearing completion of its first full schema.
Returning to liability risk, in particular, most models do agree that industrial classification data can inform company risk exposures and explain potential correlation in losses. If, in fact, all liability modelers want these data in some form, they may benefit from collaboration in creating a centralized data source or standardized data schema. Speaking in a press release with AIR (2017), Lloyd's Performance Management Director Jon Hancock appears to recognize this point:
Exactly what data to collect still remains the question. Again, the modeling community presently lacks consensus and, therefore, lacks standards, both for models and for data. While models may remain diverse, all parties again may benefit from at least agreeing on what data to collect over time.
Summary
Towers Watson (2011) published what is arguably the first description of a method for modeling liability catastrophe less than 10 years ago. In the short time since, ideas have proliferated, with brokers, reinsurers, and dedicated vendors all providing alternative views. Each of the available models undoubtedly provides important insights into risks that were formerly poorly understood, but the field is far from mature. Modelers may find that they can move faster by working together where they have common data needs. Ultimately, to achieve wider acceptance and allow the industry to identify standards, models will have to become more comparable and accountable to their results.
Acknowledgments
I would like to thank Sally Embrey and Fred Kipperman for providing insightful comments on the paper and Jack Gibson for inviting me to write it. Much of the analysis here also owes a debt to workshop participants at the September 2017 "Best Practices in Scenario Development and Usage: Present and Future" at Cambridge University—thank you for sharing your ideas and providing a critical discussion of the field.
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