Annual Loss Ratio Research Articles

Underwriting Cycles in Property-Casualty Insurance: The Impact of Catastrophic Events

This paper challenges the question of existence and predictability of underwriting cycles in the U.S. property and casualty insurance industry. Using an approach in the frequency domain, we demonstrate the existence of a hidden periodic component in annual aggregated loss ratios. The data support an underwriting cycle length of 8–9 years. Going beyond previous research and studying almost 30 years of quarterly underwriting data, we can improve forecasting performance by (dis)connecting cycles and catastrophic events. Superior out-of-sample forecast results from models with intervention variables flagging the time point of catastrophic outbreaks is achieved in terms of mean squared/absolute forecast errors. We evaluate model confidence sets containing the most accurate model with a certain confidence level. The analysis suggests that reliable forecasts can be achieved net of the irregular major peaks in loss distributions that arise from natural catastrophes as well as unusual “black swan” events.

Infill Variability and Modelling Uncertainty Implications on the Seismic Loss Assessment of an Existing RC Italian School Building

Past earthquake evidence has shown the high vulnerability of Italian school buildings, given by the extensive damage observed to structural and non-structural elements. Such vulnerability demonstrates the need to undertake a seismic risk assessment and reduction strategies for critical facilities and allocation of national funds for retrofit interventions to those regions where seismic risk is higher. To do so, Expected Annual Losses (EAL) are evermore considered one of the main seismic risk metrics, which can, however, be largely affected by the epistemic uncertainty that typically characterizes the material and geometrical properties of existing buildings, particularly masonry-infilled reinforced concrete (RC) ones. This paper investigates the implications of accounting for a thorough identification of sources and characterization of uncertainty in seismic loss estimates on the risk assessment of a typical Italian masonry-infilled RC school building. The variability in masonry infill properties and modeling assumptions, as well as the subsequent epistemic uncertainty, are explicitly considered in the loss estimation of the RC school building. Specifically, the impact on the expected annual loss ratio is quantified in terms of both structural and non-structural components, depending on the engineering demand parameter to which they are sensitive. The results show that, when considering the uncertainty related to the variability in masonry infills, higher loss ratios of up to 30% are obtained with respect to the available literature estimates.

Development of a fragility and vulnerability model for global seismic risk analyses

Seismic fragility and vulnerability assessment is an essential step in the evaluation of probabilistic seismic risk. Ideally, models developed and calibrated for the building portfolio of interest would be readily available. However, the lack of damage data and insufficient analytical studies lead to a paucity of fragility and vulnerability models, in particular in the developing world. This study describes the development of an analytical fragility and vulnerability model covering the most common building classes at the global scale. Nearly five hundred functions were developed to cover the majority of combinations of construction material, height, lateral load resisting system and seismic design level. The fragility and vulnerability were derived using nonlinear time-history analyses on equivalent single-degree-of-freedom oscillators and a large set of ground motion records representing several tectonic environments. The resulting fragility and vulnerability functions were validated through a series of tests which include the calculation of the average annual loss ratio for a number of locations, the comparison of probabilities of collapse across all building classes, and the repetition of past seismic events. The set of vulnerability functions was used for the assessment of economic losses due to earthquakes as part of the global seismic risk model supported by the Global Earthquake Model Foundation.

Influence of the multi-pulse near-fault earthquake motion on the seismic risk evaluation for reinforced concrete bridge

The multi-pulse near-fault earthquake motion imposes unique influence on the seismic risk for bridge structure. Regarding the different character of multiple pulse-like waveforms embedded in the near-fault seismic signal, the mother wavelet in wavelet analysis should be adaptively selected for best representation of the embedded multi-pulse seismic signal. A novel adaptive mother wavelet selection procedure is proposed to identify the optimum mother wavelet for each dominant pulse. The seismic risk for the example bridge system is analyzed by incremental dynamic analysis. The result indicates that the identified most unfavorable seismic signal dominates the bridge system fragility compared with the recorded horizontal signals. The top and bottom boundary of the expected annual loss ratio of the unfavorable seismic signal is 4.67% and 6.22% larger than the average value of recorded horizontal signals, respectively. It is necessary to consider the influence of the identified unfavorable seismic signal on the seismic risk for the bridge system compared with the recorded horizontal seismic signals.

Comparative earthquake loss estimations for high-code buildings in Istanbul

The paper presents the probabilistic and scenario based earthquake loss estimations for the case that the hazard and building inventory inputs are kept the same whereas the damage functions as well as the seismic demand estimation method are changed in an earthquake loss model. Spectral acceleration-displacement based damage assessments by alternating damage functions and inelastic demand evaluation methods are performed for high-code buildings in Istanbul. The buildings are mid- and high-rise, reinforced concrete, moment-resisting frames that are assumed to be designed in accordance with the provisions of Turkish Earthquake Resistant Design Code (1998). Three damage models, i.e. structural capacity and fragility curves, are employed for each building class: Expert judgment based capacity and fragility functions; HAZUS's high-code seismic design level capacity and fragility functions; and Capacity and fragility functions derived based on nonlinear analyses of code complying RC frames. Inelastic spectral displacement demands are computed with three methods: Capacity Spectrum Method, Modified Acceleration-Displacement Response Spectrum Method, and Displacement Coefficient Method. Analyses are realized under site-specific ground motions based on a state-of-the-art hazard model for eight return periods ranging from 100 to 2475 years as well as for an Mw = 7.5 scenario earthquake. Probabilistic loss curves for each case are developed. Estimated average annual losses (AAL) and loss ratios (AALR) are compared. Grid and district based maps illustrating the spatial distributions of estimated long term average losses per year and the loss ratios are presented. The estimated annualized loss ratios at district level in the city are compared to the earthquake insurance premium rates.

Cost-Benefit Analysis of Seismic Mitigation Measures for Wine Barrel Stacks

This study conducts a cost-benefit analysis of alternative seismic risk mitigation methods for wine barrel stacks. The Chilean wine industry is presented as an illustrative case study in which performance metrics, such as the expected annual loss (EAL) and benefit-cost ratios, are computed for wineries at different locations. By computing seismic risk within a consistent framework, this study shows the value of cost-benefit simulations for defining the best mitigation strategies and allocating economic resources. Likewise, this approach helps communicate information to decision makers because it is presented in a simple and transparent way, even if they are not familiar with formal risk studies. For three-level wine barrel stacks, it was observed that the Cradle Extender® (MS1) prevents a large number of barrel collapses and provides the highest benefit-cost ratio. On the other hand, for six-level wine barrel stacks, the prestressed cable (MS2) is more effective than MS1 as it prevents the barrel stack from overturning. No significant loss reduction is apparent in four- and five-level wine barrel stacks with the use of mitigation strategies; indeed, the mitigation strategies could generate greater losses and, therefore, other alternatives must be proposed.

Modeling Financial Losses Resulting from Tornadoes in European Countries

Abstract Tornadoes are a notorious, common threat to human life and property in the United States. Although less common, violent tornadoes are also reported in Europe. The authors aim for an estimation of the average annual loss ratio of European buildings due to tornadoes. An aggregated loss model is used that takes as input the tornado intensity distribution over the Fujita scale (F scale), the distribution of tornado footprint sizes per F class, the vulnerability of European buildings, and the average occurrence rate of tornadoes. Information about these variables is taken from the European Severe Weather Database and, where needed, from the U.S. Storm Prediction Center tornado database, which contains about 16 times more records. However, both databases are biased. Weak tornadoes are underrepresented. Therefore a bias-corrected tornado intensity distribution is used, with its uncertainty taken from the literature. Individual tornadoes are modeled as moving Rankine vortices creating elliptic footprints with correlated length and width. This allows for the estimation of the area fraction of a tornado footprint with lower wind speeds than the maximum wind speed, which is generally used to attribute an intensity. This approach is applied to define effective vulnerability functions of European buildings. A major result is that an expected 90% of the tornadoes contribute only about 1% to the average loss, while the rare F4 tornadoes contribute more than 40% of losses. Given that most national tornado databases in Europe contain tornado records for recent years only and few (if any) violent tornadoes, observed losses can lead to a remarkable underestimation of tornado risk in Europe.

Administrative Efficiency, Clearinghouse Exchanges, Rate Review, and Zero Profits to Limit Healthcare Insurance Premium Increases

Background: The United States spends 18% of gross domestic product, the largest proportion globally, on healthcare. American healthcare administration costs two to five times more than other high-income nations, which is transferred to the public as health insurance premium price difference. Improved healthcare access is an underlying tenet of the Affordable Care Act (ACA), however inflated health insurance premiums could reduce healthcare access. Methods: This review is based on Google, Google scholar, and PubMed literature searches performed in February 2016, to analyze rising health insurance premiums as an area for health system reform within the context of the current health system. Subsequent literature search in October 2016, confirmed the original analysis. Results and Conclusions: Except for those whose income is less than 176% of the federal poverty level selecting the minimum premium bronze plan, despite subsidies, post-ACA premiums are greater than previous out-of-pocket costs for the insured. Excessive healthcare insurance premium prices decrease healthcare access. Implementation of zero profit margins for health insurers, maximum 14% health insurer administrative cost, and universal health insurer eligibility for reinsurance, universal health insurance annual loss ratio requirements, Medicare and Medicaid prescription drug price control, and universal clearinghouse strategy health exchanges should reduce healthcare insurance premium prices. The net effect should be improved healthcare access for all Americans, not just Americans living at 175% or less of the federal poverty level. The unchanged 62% medical bankruptcy rate in 2007 and 2015 may reflect overall unimproved financial security and healthcare accessibility provided by the ACA.

Field and laboratory experiments on high dissolution rates of limestone in stream flow

Field and laboratory experiments were performed to examine dissolution rates of limestone in stream flow. Field experiments were conducted in three stream sites (A–C) with different lithological or hydrological settings around a limestone plateau in the Abukuma Mts., Japan. Sites A and B are allogenic streams, which flow from non-limestone sources into dolines, and site C has a karst spring source. Tablets made of limestone from the same plateau with a diameter of 3.5cm and a thickness of 1cm were placed in the streams for 3years (2008–2011) where alkalinity, pH and major cation concentrations were measured periodically. The saturation indices of calcite (SIc) of stream water were −2.8±0.4 at site A, −2.5±0.4 at site B and −0.5±0.4 at site C. Annual weight loss ratios for tablets were extremely high at site A (0.11–0.14mgcm−2d−1), high at site B (0.05mgcm−2d−1), and low at site C (0.005mgcm−2d−1). The contrasting rates of weight loss are mainly explained by chemical conditions of stream water. In addition, laboratory experiments for dissolution of limestone tablets using a flow-through apparatus revealed that flow conditions around the limestone tablet is another important factor for dissolution in the stream environment. These results revealed that limestone dissolves at a rapid rate where water unsaturated to calcite continuously flows, such as in an allogenic stream.

Annual risk assessment on high-frequency debris-flow fans

An empirical model of debris-flow risk assessment is developed to estimate annual loss ratio on high-frequency debris-flow fans where more than one hazard events occur every year. Based on observations of debris flows in Jiangjia Ravine, Yunnan Province, China, it is found that Gamma distribution is more appropriate for describing the annual frequency than the exponential distribution, which is supposed to be a good description of the low-frequency cases. Further analyses reveal that the two parameters of Gamma distribution can be explained, respectively, as the number of factors which dominate debris-flow occurrence and one-third of the mean annual frequency. Given the expectation of loss ratio is unchanged for each event we deduced a simple relationship between the expectations of one-event and annual loss ratios. Combined with the Gamma model, an equation is proposed to calculate the expectation of the annual loss ratio, which can be also used to assess the potential risk of fans formed by high-frequency debris flows.

Runoff and Soil Loss Response to Vegetation Removal in a Semiarid Environment

AbstractThe removal of vegetation is the main cause of soil degradation in semiarid areas. We hypothesized that the changes in soil properties induced by vegetation removal modified the runoff and soil erosion response in a semiarid area of Spain. To test this, two plots (15 by 5 m) were installed on a 23% slope on a Lithic Haploxeroll. Vegetation was removed by clipping from one of the plots (Plot D) and the changes in surface runoff and soil loss were compared with an undisturbed control plot (Plot N) from 1989 to 1993. Total runoff was significantly greater in Plot D (48.8 mm) than in Plot N (34.9 mm). Runoff ratios between the disturbed and natural plots increased with time from 1.4:1 in 1990 to 2.5:1 in 1993. Vegetation removal increased the soil losses in Plot D (150.2 g m−2) by 127% compared with those in Plot N (66.3 g m−2). The annual soil loss ratio between the disturbed and natural plots increased from 1.6:1 in 1989 to 4.2:1 in 1993. The observed increase in surface runoff and soil loss was attributed to a progressive deterioration of soil physical properties in Plot D. Bulk density increased by 8.4% (from 1.55 to 1.68 Mg m−3) and a reduction of total organic carbon (from 4.0 to 2.6%) and the percentage of stable aggregates (from 81.6 to 56.3%) were observed. There was no evidence of vegetation recovery, suggesting that reduced vegetal cover might lead to irreversible soil degradation in semiarid areas.

A Comparative Economic Analysis of Tort Liability and No-Fault Compensation Systems in Automobile Insurance

Based on an analysis of annual loss ratio data by state for automobile liability insurance during 1975-1980, the economic impact of no-fault automobile insurance on the relative benefits and costs to consumers and on the predictability of relative loss costs for insurers is assessed. Several hypotheses are tested by using some regression models. The results suggest that no-fault automobile insurance tends to increase relative benefits or decrease relative costs (prices) to consumers, but in the short run it does not improve the predictability of relative loss costs for insurers. From a public policy viewpoint, these results seem to suggest that a no-fault compensation system performs more efficiently than a tort-liability system for automobile insurance consumers. I. Overview and Purpose Criticisms of the efficiency and fairness of the tort liability compensation system in automobile insurance culminated with the adoption of no-fault compensation systems in 24 states in the 1970's. No-fault automobile insurance is a first-party coverage under which each driver accepts financial responsibility for some or all losses and injuries sustained by occupants of his or her own car, pedestrians hit by his or her car, and himself or herself in exchange for partial immunity from liability for losses to third parties or other drivers and their passengers. This means that recovery of losses from automobile accidents within certain limits is available to victims without regard to fault. In contrast, under the tort liability compensation system, fault or

Comments on the Exchange between Hedges and Witt

The recent exchange between Hedges [1] and Witt [2] prompts a few additional comments. These are motivated by a concern for the misconceptions that might be created by those comments, not by a desire to take sides. Witt [3] had found a positive correlation between the temporal average of the loss ratio of automobile insurers in 51 jurisdictions and the standard deviation of the annual results from the temporal mean for each jurisdiction. The main issue in the exchange is whether one should view as surprising the fact that the correlation was positive. Hedges [1] proposes a mechanism which suggests to him that the correlation should be positive, and Witt [2] counters that the mathematical relation and institutional factors proposed by Hedges do not tend to make the correlation positive. The present comment addresses two issues: the relevance of the central limit theorem to the belief that the mean and standard deviation should be independent unless there are real, structural effects, and the relevance of the standard deviation as a measure of risk in the empirical study. Witt states: Mathematically, it can be shown that there is no relationship between the mean and variance of normally distributed random variables. Since the annual loss ratio of all the companies is nothing more than the weighted average loss ratio of all the companies writing a given coverage in a state, the Central Limit Theorem would suggest that the annual loss ratio in a state should be normally distributed. Therefore, it would seem quite reasonable to argue that there is no mathematical relationship between the mean and the variance of the annual loss ratios in a state. [2] This argument is not valid.

The Underwriting Risk and Return Paradox Revisited

Recently, Witt [7,8] suggested that one would expect to find a negative or inverse relationship between mean state loss ratios and standard deviations of the associated annual loss ratios by state for automobile insurance if underwriting risk (as measured by the standard deviation of loss ratios in a state) were properly included in insurance rates, other things being equal. However, based on an empirical test of this hypothesis, he found a direct rather than an inverse relationship between these variables. Hedges [3] later argued that the observed positive relationship could have resulted from a mathematical relationship between the average loss ratios and standard deviations and/or from certain institutional factors which affect loss ratios and insurance rates in the various states. Based on some empirical tests of economic and institutional factors, Witt [9] showed that Hedges' institutional hypothesis could not be verified. His regression results for the whole industry showed a positive relationship between the underwriting risk and return variables even after he included various economic and institutional variables in the regression model. The regressions for the direct-writing, national-agency, and regional-speciality companies also revealed a positive relationship between the means and standard deviations of loss ratios by state. Thus. the addition of some institutional variables to his regression model did not reverse the significant positive relationship between mean loss ratios and standard deviations by state. Accordingly, he argued that the perverse observed positive correlation could not be easily explained by differences in institutional factors among states.' In regard to Hedges' mathematical hypothesis, Witt [91 argued that if the annual loss ratios by state are normally distributed there should be no relationship between the averages and the standard deviations of these ratios because there is no mathematical relationship between the mean and variance of a normally distributed random variable. Witt indicated that the Central Limit Theorem would suggest that the annual loss ratio in a state should be normally distributed because it is nothing more than the weighted average loss ratio of all the companies writing a given coverage in the state. Hence, he argued the positive correlations he observed could not be reasonably explained by the

Author's Reply: Underwriting Risk and Return: Some Additional Comments

In a recent paper, the author suggested that one would expect to find an inverse relationship between mean loss ratios and standard deviations of the associated annual loss ratios by state for automobile insurance if this coverage were properly priced.1 In other words, one would expect lower underwriting profits to be associated with higher loss ratios, and therefore, a company would have to anticipate lower underwriting risk in order to have an economic incentive to sell automobile insurance in such states. Accordingly, one would expect that the average loss ratios and standard deviations for a given coverage in the various states would vary inversely with each other if underwriting risk were properly reflected in the insurance rates for the coverage, other things being equal. In order to test this economic hypothesis for various automobile insurance coverages, the correlation coefficient between the mean loss ratios and standard deviations for the various states was calculated to determine if an inverse or negative relationship existed. However, a positive rather than a negative relationship was found between these variables. The author found this empirical relationship to be somewhat surprising.