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Natural Catastrophe Risk and the Changing Environment: Overview and Challenges Shree Khare, Senior Catastrophe Risk Modeller, RMS Ltd., London

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2Confidential Talk Outline qFocus: Hurricane Risk Modelling –Financial motivation –Catastrophe modelling basics: Event set framework –Components –Climate change –Model development project qMathematical and scientific challenges Opportunities for collaboration

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3Confidential Introduction to RMS q qFounded at Stanford University in 1988 q qMulti-disciplinary skills: Applied mathematics, statistics, physical sciences and engineering applied to insurance q qSolely focused on risk management issues q qIndependent and objective information source q qGlobal presence in major insurance markets At RMS, our goal is to help clients manage catastrophe risk through the practical application of the most advanced quantitative risk assessment techniques available. - Hemant Shah, President & CEO

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4Confidential Top 10 Insured Cat Losses, 1990-2005 * Includes liability losses CountryEventYearInsured Loss ($billions) Indonesia, Thailand U.S., Bahamas France, Switzerland France, U.K. Japan U.S., Caribbean U.S. U.S., Bahamas U.S. Earthquake & Tsunami Hurricane Wilma Winterstorm Lothar Winterstorm Daria Typhoon Mireille Hurricane Charley Hurricane Ivan Northridge Earthquake Hurricane Andrew Terrorist Attack on WTC 2004 2005 1999 1990 1991 2004 1994 1992 2001 5.0 6.5 6.6 7.8 8.0 11.0 17.8 21.5 31.7* U.S.Hurricane Katrina200545.0 6.0-6.8 Swiss Re Sigma 2/2006; Triple I 1/2006

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5Confidential Framework: Event Based Modelling Assess Wind Speed - Peak gusts experienced at each location Calculate Damage - Varies by structure type Define Hurricane - -Track - -intensity Quantify Financial Loss - Apply policy terms and Reinsurance structures $ Loss Apply property exposure q qUsing physical and statistical modelling - simulate events in time and quantify financial loss for each event q qModel components are consistent with observed data

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6Confidential Framework: Event Based Modelling Assess Wind Speed - Peak gusts experienced at each location Calculate Damage - Varies by structure type Define Hurricane - -Track - -intensity Quantify Financial Loss - Apply policy terms and Reinsurance structures $ Loss Apply property exposure q qSimulation of hundreds of thousands of years can be used to quantify modelled probabilities of financial loss

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7Confidential Framework: Event Based Modelling Assess Wind Speed - Peak gusts experienced at each location Calculate Damage - Varies by structure type Define Hurricane - -Track - -intensity Quantify Financial Loss - Apply policy terms and Reinsurance structures $ Loss Apply property exposure q qModel output is used to inform Enterprise Risk Management: Rate setting, capital allocation, securities …

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8Confidential Hurricane Risk Model Components qRates (5-year view, long-term projections in a changing climate) qTrack modelling: Trajectories of tropical vortices in space/time qWindfield qSurface roughness and topography qTransitioning of tropical extra-tropical storms qVulnerability qExposure qFinancial Model qOn the horizon: Parametric and model-choice uncertainty

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9Confidential qNeed to quantify expected number of landalling hurricanes: models are validated using historical data Data source: NOAA NHC HURDAT Best Track 1950-2005: 597 time series for named North Atlantic TCs Modelling Hurricane Rates

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10Confidential qInsurance/Re-insurance industry typically interested in 5-year projections Data source: NOAA NHC HURDAT Best Track 1950-2005: 597 time series for named North Atlantic TCs Modelling Hurricane Rates

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11Confidential Modelling Hurricane Rates Cat 1-5 Storms Blue Basin Numbers Red Landfall Numbers HURDAT data Jarvinen et al. (1984) q qRMS has built an exhaustive collection of statistical models for predicting this non-stationary time series q qAnnually, we gather world-leading hurricane experts to give us their recommendations as to which of our models are best for predicting future rates (expert elicitation)

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12Confidential Modelling Hurricane Tracks For most diagnostics in most regions (but not all) the historical TCs fall within the range of values in the synthetic TC set (Hall and Jewson, Tellus, 2007). Evaluation criterion: historical TCs should be statistically indistinguishable from equal-sized samples of synthetic TC set. On most coast regions track models landfall predictions beat predictions derived solely from local landfall events, based on out-of-sample likelihood analysis (Hall and Jewson, JAM, 2007). HISTORICAL (1950-2005)SYNTHETIC (1000 YRS)

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13Confidential Long-Term Risk Management: Climate Change

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14Confidential Long-Term Risk Management: Climate Change q qNatural forcing can not explain 20 th century warming

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15Confidential Rates and Track Modelling in a Changing Climate qClients are increasingly interested in quantifying hurricane risk in future climates qGiven the changing climate, quantifying future risk is a significant challenge (more later …)

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16Confidential Model Development Example: Hurricane Winds qNatural catastrophe risk models are comprised of components (rates, track, winds, …) qNeed to generate millions of simulations qNeed to explore efficient methods of generating windfields along the modelled tracks qGiven some validation data set, can use cross-validation to perform model selection qQuick overview of hurricane vortex model comparison qApologies in advance for jargon …

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17Confidential qGoal: To model maximum 1-minute/3-second winds over ocean and land (10 m height with roughness) for a large number of simulated events qGiven spatial scales of hurricanes, full 3-dimensional numerical modelling can not feasibly be used to generate the full stochastic set Model Development Example: Hurricane Winds

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18Confidential Wind Modelling Basics qWe need some approximations: Steady Pressure Field qHeating source maintains a steady pressure gradient on time scales of 6 hours - also ignoring feedbacks, convection, vertical acceleration … qApproximate pressure distribution as radially symmetric: p(r)

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19Confidential Wind Models: PBL + Linear Analytical qOur interest is 10m winds: Consider the atmospheric boundary layer qSurface layer is turbulent: Ultimately arising from surface friction – has effect of slowing down winds at surface

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20Confidential Wind Models: PBL + Linear Analytical qSpace/time scales of turbulent motions can be extremely small, hence difficult to model qAttempt to model larger scale flow by Reynolds Averaging

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21Confidential Wind Models: PBL + Linear Analytical qThe (approximate) momentum equations (in translating system)

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22Confidential Wind Models: PBL + Linear Analytical qPBL (Chow, Vickery, Cardone, FHLC): Vertical mean – friction parameterization

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23Confidential Wind Models: PBL + Linear Analytical qFor Gradient Wind let H, and look at the steady state solution, which is the root (with the proper limiting property) of:

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24Confidential Linear Analytical Boundary Layer Model q qAnalytical theory developed in Kepert (2001) for 3-dimensional flow in a translating vortex for a prescribed pressure field q qModel has friction, vertical diffusion, slip boundary condition at surface

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25Confidential Linear Analytical Boundary Layer Model q qIdea: Linearize equations about gradient wind, solve first order equations q qEfficient (free) to run, encapsulates physics causing asymmetries q qz, Cd and K can be optimized

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26Confidential Model Selection Study Using H*WIND qH*WIND is consists of 10 m, 1-minute mean winds over ocean which summarizes nearly all available data (surface obs, flight level …) qPut together by researchers at Hurricane Research Division of NOAA in Miami qWe are the first group to perform such a thorough study …

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27Confidential Mathematical and Scientific Challenges: Collaboration qRMS is in a unique position, serving as an intermediary between academic/government research and the financial industry qOur models involve many components – some of which are developed through collaboration with the wider research community qThis involves pure academic research and paid consultancies qExample institutions: LSE, NASA, University of Miami, National Center for Atmospheric Research, Oxford, … qCollaboration often leads to peer-reviewed journal publications qWe work with PhD students, University Faculty, US Government Researchers, Post-Docs, … qWe are very open to new collaboration …

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28Confidential Extreme Value Theory qEVT is not often used in catastrophe risk modelling qWith event based mathematical modelling, spatially correlated extremes are naturally accounted for – a challenge in EVT qOutput from cat models may provide a rich data set to play with qCan EVT be used to gain greater insight into cat model output? qCan EVT be used to build better cat models?

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29Confidential Use of Climate Models in Catastrophe Risk qGeneral circulation models are used by research groups to simulate the evolution of future climates qClimate researchers and catastrophe risk modellers ask related, yet unique questions qIt is challenging for catastrophe risk modellers to make best use of climate simulations qHow we make best use of climate simulations will involve extensive research and statistical analysis

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30Confidential Model Choice Uncertainty qCatastrophe models are made of components qComponents have parameters, which have been estimated using observed data qFinancial loss can be sensitive to uncertain parameters – this kind of information will be included in future cat models qFinancial loss is also sensitive to choice of model components (track model A vs. track model B) qHow do we best quantify model choice sensitivity/uncertainty? qHow do we optimally use ensembles of models? qBayesian model averaging seems inadequate due to double- counting (e.g. Hoeting et al., 1999, Statistical Science) qCat modelling requires a proper statistical framework to answer these questions

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31Confidential QUESTIONS?

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