Probable Maximum Loss Research Articles

Multi-hazard direct economic loss risk assessment on the Tibet Plateau

Natural disasters are becoming increasingly regional, frequent, and complex. Semi-quantitative risk assessments based on risk indices or relative risk levels lack quantitative parameters to characterize losses adequately. This study focuses on earthquakes and geological disasters, quantitatively assessing the risk of probable maximum loss (PML) from multi-hazard on the Tibet Plateau (TP) in terms of both absolute and relative values. The results indicate that total PML from multi-hazard on the TP is estimated at 465.5 billion CNY, with a relative value of 5.3%. The total loss value of towns with very high absolute PML is estimated at 254.8 billion CNY, while the relative loss value of towns with very high relative PML is 25.1%. Towns with high absolute value of PML for multi-hazard may have higher fixed asset values, while those with high relative value imply higher vulnerability. Adjusting building structures and reducing the vulnerability of buildings could effectively mitigate the risk of disaster losses caused by multiple hazards.

A probabilistic estimation model for seismic physical portfolio loss of a water supply pipeline system

Losses due to hazards are inevitable and numerical simulations for estimations are complex. This study proposes a model for estimating correlated seismic damages and losses of a water supply pipeline system as an alternative for numerical simulations. The common approach in other research shows average damage spots per mesh estimated statistically independent to one another. Spatially distributed lifeline systems, such as water supply pipelines, are interconnected, and seismic spatial variability affects the damages across the region; thus, spatial correlation of damage spots is an important factor in target areas for portfolio loss estimation. Generally, simulations are used to estimate possible losses; however, these assume each damage behaves independently and uncorrelated. This paper assumed that damages per mesh behave in a Poisson distribution to avoid over-dispersion and eliminate negative losses in estimations. The purpose of this study is to obtain a probabilistic portfolio loss model of an extensive water supply area. The proposed model was compared to the numerical simulation data with the correlated Poisson distribution. The application of the Normal To Anything (NORTA) obtained correlations for Poisson Distributions. The proposed probabilistic portfolio loss model, based on the generalized linear model and central limit theory, estimated the possible losses, such as the Probable Maximum Loss (PML, 90% non-exceedance) or Normal Expected Loss (NEL, 50 % non-exceedance). The proposed model can be used in other lifeline systems as well, though additional investigation is needed for confirmation. From the estimations, a seismic physical portfolio loss for the water supply system was presented. The portfolio was made to show possible outcomes for the system. The proposed method was tested and analyzed using an artificial field and a location-based scenario of a water supply pipeline system. This would aid in pre-disaster planning and would require only a few steps and time.

Seismic resilience assessment of buildings: A simplified methodological approach through conventional seismic risk assessment

A simplified methodology to evaluate seismic resilience of buildings through a probabilistic risk assessment is proposed. The methodology uses the results from the conventional seismic risk assessment with the inclusion of social and economic aspects. The seismic resilience assessment process considers the workforce population, repair time, direct and indirect losses. They can be applied within the damage definition stage with the aim of the vulnerability functions for a specific building typology, and loss estimation stage of the probabilistic risk assessment. For the case of the definition of vulnerability functions a previous methodological approach is used with fewer modifications. In addition, a new risk figure called average annual repair time is introduced in the probabilistic risk assessment allowing to obtain the resilience index. Aspects such as expected repair time, quantities of crew members, business interruption losses, workforce population capacity and risk figures: average annual loss, probable maximum loss and average annual repair time are considered. Then, all those aspects are integrated within the exposure, damage, and loss estimation models with additional considerations to perform the calculation of the resilience. Finally, the results are represented by means of a unitless simplified resilience index allowing to be compared among different scenarios. The methodology is illustrated using two study cases. The first one represented its application at damage definition stage and is comprised by 3-, 6- and 9-story reinforced concrete moment resisting frame school buildings designed for special seismic code level. The second one covered the application at loss estimation stage and considers a fictitious portfolio of approximately 190,000 buildings composed by the previous three building typologies located along the whole country of Peru. The results show a highly sensitivity associated to workforce population, repair time, and indirect losses. Conclusions and possible applications related to Disaster Risk Reduction are summarized.

Accessing Insurance Flood Losses Using a Catastrophe Model and Climate Change Scenarios

Impact Forecasting has developed a catastrophe flood model for Czechia to estimate insurance losses. The model is built on a dataset of 12,066 years of daily rainfall and temperature data for the European area, representing the current climate (LAERTES-EU). This dataset was used as input to the rainfall–runoff model, resulting in a series of daily river channel discharges. Using analyses of global and regional climate models dealing with the impacts of climate change, this dataset was adjusted for the individual RCP climate scenarios in Europe. The river channel discharges were then re-derived using the already calibrated rainfall–runoff models. Based on the changed discharges, alternative versions of the standard catastrophe flood model for the Czechia were created for the various climate scenarios. In outputs, differences in severity, intensity, and number of events might be observed, as well as the size of storms. The effect on the losses might be investigated by probable maximum losses (PML) curves and average annual loss (AAL) values. For return period 1 in 5 years for the worst-case scenario, the differences can be up to +125 percent increase in insurance losses, while for the return period 1 in 100 years it is a −40 percent decrease. There is no significant effect of adaptation measures for the return period 1 in 100 years, but there is a −20 percent decrease in the return period 1 in 5 years.

Parametric Insurance—A Possible and Necessary Solution to Insure the Earthquake Risk of Romania

The rapid growth over recent decades of the impact of natural disasters on economies, especially in vulnerable areas, urges stakeholders to promote innovative solutions involving risk transfers that account for the new risk exposures. These proposed solutions are designed to optimize and expedite the indemnification process, which can ultimately be beneficial for both policyholders and insurers alike. This article explores the possibility of supplementing the current Romanian dwelling insurance protection scheme with a parametric mechanism. To determine the triggering parameter of the insurance pay-out, the authors consider various hazard scenarios developed based on historical events. This paper focuses on Probable Maximum Loss (PML) determination computed for events with epicenters in the Vrancea (a region and a mountain in the Carpathians) seismic area. This area is the most exposed in Romania to earthquakes, and it includes the capital, Bucharest, which is the urban area with the highest population concentration and, consequently, the highest exposure to the discussed risks.

A Nonproportional Premium Rating Method for Construction Risks

Correct pricing of nonproportional (primary or excess of loss) insurance for construction risks must consider not only how the insured property values build up over time, but also how the probable maximum loss (PML) changes. Conventional pricing methods for static property risks cannot be employed for construction risks, since the latter are characterized by PML patterns that change over time, as well as evolving loss exposures and perils arising from the various phases of the construction project. A further complication arises when delay in startup (DSU) is covered, because a DSU loss is triggered by a property damage loss and both losses contribute jointly to the erosion of an excess layer. This article describes a pricing method with analysis of specific cases of interest, including guidelines for creating practical excess of loss rating models.

Extreme Data Breach Losses: An Alternative Approach to Estimating Probable Maximum Loss for Data Breach Risk

This study proposes a measure of the data breach risk’s probable maximum loss, which stands for the worst data breach loss likely to occur, using an alternative approach to estimating the potential loss degree of an extreme event with one of the largest private databases for data breach risk. We determine stationarity, the presence of autoregressive feature, and the Fréchet type of generalized extreme value distribution (GEV) as the best fit for data breach loss maxima series and check robustness of the model with a public dataset. We find that the predicted data breach loss likely to occur in the next five years is substantially larger than the loss estimated by the recent literature with a Pareto model. In particular, the comparison between the estimates from the recent data (after 2014) and those for the old data (before 2014) shows a significant increase with a break in the loss severity. We design a three-layer reinsurance scheme based on the probable maximum loss estimates with public–private partnership. Our findings are important for risk managers, actuaries, and policymakers concerned about the enormous cost of the next extreme cyber event.

Seismic vulnerability assessment of precast RC industrial buildings in Turkey

In seismic risk assessment, the fragility curves are commonly used to express the probability of exceedance of the predetermined damage states as the function of the earthquake ground motion parameter for structures. In this paper, the seismic vulnerability of single story precast reinforced concrete industrial buildings located in the organized industrial zones in Turkey were studied. The 273 existing buildings located in the different regions of Turkey were surveyed to get their geometry and structural parameters and 80 model types were identified. The effects of the structural parameters on the structural damage were studied via the fragility curves. The damage index parameter was used in the analytically obtained fragility curves for the four damage states as a function of spectral acceleration. Two sets of ground motion records were used representing the soft and stiff site conditions in the incremental dynamic analysis. The aim of this study is to obtain mean fragility curves for the three main classes of industrial precast reinforced concrete building structures, namely the Poor, Typical and the Superior. The structural parameters of stiffness, ductility and strength were used in the classification of the buildings. The study has focused on the probable maximum loss estimation for the above three building classes. The results indicate a good compatibility with the observed damages in the past earthquakes. It is believed that the proposed study can be used for seismic risk assessment based on the spectral acceleration levels experienced by these single story precast reinforced concrete industrial buildings.

Probable maximum loss of a pipe network due to earthquakes: a case study in Iloilo city, Philippines

PurposeBuried structures like pipeline systems or water distribution networks (WDN) are vulnerable to seismic activities and the risk of damages increases when there is liquefaction. This paper aims to propose a methodology on how to determine the probable maximum loss (PML) on pipeline systems when earthquakes and liquefaction occur in future scenarios.Design/methodology/approachThe paper used historical data and presents a case study on how the methodology to estimate the PML was used. The estimation is analytic and relied on simulations to determine the seismic and liquefaction hazard in the study area. Statistical and numerical analysis was used to estimate the damages and losses.FindingsThe output shows the PML of a WDN at different earthquake scenarios. It also shows a comparison between the damages and losses of diameter sizes of the pipes.Research limitations/implicationsIn this paper, the damages behaved independently in one area, and correlation was not considered.Practical implicationsThis PML methodology can aid in pre-disaster planning to prepare for seismic countermeasures risk transfer such as insurance to reduce the loss.Originality/valueThis paper shows a methodology and example on how to estimate the damages and PMLs of an existing WDN of a projected earthquake and liquefaction hazard based on historical data.

Information asymmetry and the inefficiency of informal ip strategies within employment relationships

Employee mobility and betrayal increase the risks of disclosing unpublished technical information. This study builds a theoretical foundation for the loss of unpublished technical information regarding human capital. It analyzes the inefficiency of informal intellectual property (“IP”) strategies, which include non-disclosure agreements (“NDAs”), covenants not to compete (“CNCs”), and trade secrets, from the maximum probable loss approach. It bridges the legal literature and the economics literature by emphasizing and explaining the information asymmetries in employment relationships regarding the informal IP strategies. NDAs need to be supplemented by CNCs or trade secret law. Enforceable CNCs and trade secrets have a reward function, but trade secrets are more efficient in informal IP management and innovation. Beyond the legal risks imposed by informal IP, companies should actively improve employee loyalty and their security culture through employee management.

Time-Consistent Asymptotic Exponential Arbitrage with Small Probable Maximum Loss

Based on a concept of asymptotic exponential arbitrage proposed by Follmer-Schachermayer, the author introduces a new formulation of asymptotic arbitrage with two main differences from the previous one: Firstly, the realising strategy does not depend on the maturity time while the previous one does, and secondly, the probable maximum loss is allowed to be small constant instead of a decreasing function of time. The main result gives a sufficient condition on stock prices for the existence of such asymptotic arbitrage. As a consequence, she gives a new proof of a conjecture of Follmer and Schachermayer.

Value-at-Risk and Models of Dependence in the U.S. Federal Crop Insurance Program

The federal crop insurance program covered more than 110 billion dollars in total liability in 2018. The program consists of policies across a wide range of crops, plans, and locations. Weather and other latent variables induce dependence among components of the portfolio. Computing value-at-risk (VaR) is important because the Standard Reinsurance Agreement (SRA) allows for a portion of the risk to be transferred to the federal government. Further, the international reinsurance industry is extensively involved in risk sharing arrangements with U.S. crop insurers. VaR is an important measure of the risk of an insurance portfolio. In this context, VaR is typically expressed in terms of probable maximum loss (PML) or as a return period, whereby a loss of certain magnitude is expected to return within a given period of time. Determining bounds on VaR is complicated by the non-homogeneous nature of crop insurance portfolios. We consider several different scenarios for the marginal distributions of losses and provide sharp bounds on VaR using a rearrangement algorithm. Our results are related to alternative measures of portfolio risks based on multivariate distribution functions and alternative copula specifications.

Changes in Tsunami Risk to Residential Buildings at Omaha Beach, New Zealand

Coastal settlements worldwide have suffered significant damage and loss to tsunami hazards in the last few decades. This period coincides with socio-economic changes that have heightened spatio-temporal risk through increased coastal development and infrastructure. In this study, we apply a spatio-temporal loss model to quantify the changes in direct economic losses to residential buildings from tsunami hazards over a 20-year period in Omaha Beach, New Zealand. The approach reconstructed temporal urban settlement patterns (1992, 1996, 2006 and 2012) for an area potentially exposed to regional source tsunami inundation hazard. Synthetic depth–damage functions for specific building classes were applied to estimate temporal damage and loss from tsunami inundation exposure at each building location. Temporal loss estimates were reported for a range of risk metrics, including probable maximum loss, loss exceedance and average annual loss. The results showed that an increase in the number of buildings and changes to building design (i.e., storeys, floor area, foundations) influenced the increasing risk to direct economic loss over the study period. These increases were driven by conversion from rural to urban land use since 1996. The spatio-temporal method presented in this study can be adapted to analyse changing risk patterns and trends for coastal settlements to inform future tsunami mitigation measures and manage direct economic losses.

Probabilistic seismic vulnerability and loss assessment of the residential building stock in Costa Rica

This study presents a seismic vulnerability and risk assessment of the residential building stock in Costa Rica. It proposes a new exposure model using housing census data, public construction statistics, and private construction information to quantify and characterize the residential building portfolio. A complete vulnerability catalogue is established by developing fragility functions for the most common building classes and combining them with existing models derived for risk assessment in South America. An existing probabilistic seismic hazard model was implemented within the OpenQuake-engine, and complemented with a simplified site model to account for site effects. Earthquake risk assessment is achieved by means of a probabilistic event-based analysis, which allowed the estimation of several risk metrics. These include average annualized losses at a national scale, disaggregated per building class and administrative regions. The probable maximum losses and exceedance probability curves were generated using a stochastic event set with 100,000 years of events per logic tree branch.

Development of innovative methods for risk assessment in high-rise construction based on clustering of risk factors

The article analyses risks in high-rise construction in terms of investment value with account of the maximum probable loss in case of risk event. The authors scrutinized the risks of high-rise construction in regions with various geographic, climatic and socio-economic conditions that may influence the project environment. Risk classification is presented in general terms, that includes aggregated characteristics of risks being common for many regions. Cluster analysis tools, that allow considering generalized groups of risk depending on their qualitative and quantitative features, were used in order to model the influence of the risk factors on the implementation of investment project. For convenience of further calculations, each type of risk is assigned a separate code with the number of the cluster and the subtype of risk. This approach and the coding of risk factors makes it possible to build a risk matrix, which greatly facilitates the task of determining the degree of impact of risks. The authors clarified and expanded the concept of the price risk, which is defined as the expected value of the event, 105 which extends the capabilities of the model, allows estimating an interval of the probability of occurrence and also using other probabilistic methods of calculation.

Probabilistic Seismic Risk Assessment in Manizales, Colombia: Quantifying Losses for Insurance Purposes

A fully probabilistic seismic risk assessment was developed in Manizales, Colombia, considering assets of different types. The first type includes elements that are part of the water and sewage network, and the second type includes public and private buildings. This assessment required the development of a probabilistic seismic hazard analysis that accounts for the dynamic soil response, assembling high resolution exposure databases, and the development of damage models for different types of elements. The economic appraisal of the exposed assets was developed together with specialists of the water utilities company of Manizales and the city administration. The risk assessment was performed using several Comprehensive Approach to Probabilistic Risk Assessment modules as well as the R-System, obtaining results in terms of traditional metrics such as loss exceedance curve, average annual loss, and probable maximum loss. For the case of pipelines, repair rates were also estimated. The results for the water and sewage network were used in activities related to the expansion and maintenance strategies, as well as for the exploration of financial retention and transfer alternatives using insurance schemes based on technical, probabilistic, and prospective damage and loss estimations. In the case of the buildings, the results were used in the update of the technical premium values of the existing collective insurance scheme.

Probable Maximum Loss for the Florida Public Hurricane Loss Model: Comparison

AbstractHurricanes are a way of life in South Florida, where owning a home without windstorm insurance is almost an impossibility. Insurance premiums for windstorm loses are computed through the us...

Cost-benefit analysis to assess seismic mitigation options in Mexican public school buildings

This study presents a methodology to perform a cost-benefit (C/B) analysis to assess possible options such as retrofitting or reconstruction of structures focused on mitigation of direct physical losses due to seismic actions. The case of all public school buildings located in Mexico City is presented as an illustrative example having as measure parameters the expected loss, the expected annual loss (EAL) and the probable maximum loss (PML). For the proposed methodology the following steps are required: (1) To gather technical information of typical school buildings designed according to different past seismic codes of the region, (2) To propose seismic mitigation actions such as retrofitting or stiffening of the structural system in order to comply with the current Mexico City seismic design code (RCDF-2004), (3) To compute vulnerability functions by carrying out non-linear Incremental Dynamic Analyses (IDA) for the original designed structural systems and those modified according to the performed mitigation actions, (4) To carry out a probabilistic seismic risk analysis taking into account all locations of public school buildings in Mexico City, (5) To perform a C/B analysis assuming two different cases: (a) retrofitting and/or stiffening the structural system and (b) demolish and reconstruct a completely new school building. This analysis is carried out at two different levels: (1) vulnerability functions of structures considering the two mitigation actions are obtained and compared, and (b) a combination of the different mitigation alternatives is investigated in order to determine, by obtaining the EAL and PML, the number and location of schools that require mitigation actions assuming that economical resources are limited. The usefulness of carrying out a C/B analysis by computing the seismic risk is shown as an aid to formulate and define mitigation strategies that allow decision-makers to prioritize the use of the economic resources. The advantage of this approach is that the obtained results will be presented in such a way they will be easier to communicate to decision-makers even if they are not familiar with formal risk studies.

Estimating extreme losses for the Florida Public Hurricane Model—part II

Rising global temperatures are leading to an increase in the number of extreme events and losses ( http://www.epa.gov/climatechange/science/indicators/ ). Accurate estimation of these extreme losses with the intention of protecting themselves against them is critical to insurance companies. In a previous paper, Gulati et al. (2014) discussed probable maximum loss (PML) estimation for the Florida Public Hurricane Loss Model (FPHLM) using parametric and nonparametric methods. In this paper, we investigate the use of semi-parametric methods to do the same. Detailed analysis of the data shows that the annual losses from FPHLM do not tend to be very heavy tailed, and therefore, neither the popular Hill’s method nor the moment’s estimator work well. However, Pickand’s estimator with threshold around the 84th percentile provides a good fit for the extreme quantiles for the losses.

Collapse Probability of a Low-rise Piloti-type Building Considering Domestic Seismic Hazard

The risk-based assessment, also called time-based assessment of structure is usually performed to provide seismic risk evaluation of a target structure for its entire life-cycle, e.g. 50 years. The prediction of collapse probability is the estimator in the risk-based assessment. While the risk-based assessment is the key in the performance-based earthquake engineering, its application is very limited because this evaluation method is very expensive in terms of simulation and computational efforts. So the evaluation database for many archetype structures usually serve as representative of the specific system. However, there is no such an assessment performed for building stocks in Korea. Consequently, the performance objective of current building code, KBC is not clear at least in a quantitative way. This shortcoming gives an unresolved issue to insurance industry, socio-economic impact, seismic safety policy in national and local governments. In this study, we evaluate the comprehensive seismic performance of an low-rise residential buildings with discontinuous structural walls, so called piloti-type structure which is commonly found in low-rise domestic building stocks. The collapse probability is obtained using the risk integral of a conditioned collapse capacity function and regression of current hazard curve. Based on this approach it is expected to provide a robust tool to seismic safety policy as well as seismic risk analysis such as Probable Maximum Loss (PML) commonly used in the insurance industry.