Modelling Uncertainty in Claims Experience to Price General Insurance Contracts Vanita Duggal Actuary Palisade Risk Conference, Mumbai January 13, 2015
What is Insurance? Coverage by contract whereby one party undertakes to indemnify or guarantee another against loss by a specified contingency or peril - Merriam Webster Equitable transfer of the risk of a loss, from one entity to another in exchange for payment. A form of risk management primarily used to hedge against the risk of a contingent, uncertain loss. - Wikipedia Palisade Risk Conference 2015, Mumbai 2
Property & Casualty (P&C) Insurance Types of Cover Property Insurance Provides indemnity against loss or damage to the insured s own property Liability Insurance Provides indemnity where the insured, owing to some form of negligence, is legally liable to pay compensation to a third party Financial Loss Indemnity against pecuniary loss from bad debts or failure of a third party Fidelity guarantee against losses by dishonest actions of employees - fraud, theft, embezzlement Other non-life covers Bloodstock (Equine), Kidnap & Ransom, Political Risk, Event, Travel Palisade Risk Conference 2015, Mumbai 3
Property & Casualty (P&C) Insurance Some Examples Property Insurance Residential buildings Home contents Commercial property Land vehicles Private Motor Commercial Fleet Aircraft, Marine craft Hull Cargo, freight Crops insurance Casualty Insurance Public Liability Product Liability Employers Liability Professional Indemnity Directors and Officers (D&O) Errors and Omissions (E&O) Medical Malpractice Motor third party Liability Environmental Liability Bodily injury Damage, clean-up costs Palisade Risk Conference 2015, Mumbai 4
Property & Casualty (P&C) Insurance Insured Perils Buildings and Contents Fire, explosion Burst pipes - water, oil, gas leaks Subsidence Natural perils - flood, storm, earthquake, lightning Theft Motor, aircraft, marine craft Fire, theft Accidents Loss or damage to the craft / cargo from impact Liability to passengers or third parties for damage, injury, death Oil spills Crops Disease Fire Weather related perils - storm, drought Palisade Risk Conference 2015, Mumbai 5
Property & Casualty (P&C) Insurance Insured Perils Public and Product Liability Slip/Trip accidents at a retail store Injury from a falling brick at a construction site Faulty design or manufacture Faulty packaging; misleading or incorrect instructions Employers Liability Accidents due to negligence of employer or other employees Exposure to harmful substances - chemicals, fumes, asbestos Harmful working conditions - loud noises, repetitive strain Professional Indemnity Litigation due to errors made by directors and officers Incorrect advice from accountants, solicitors, real estate agents, architects Error in an actuarial report Wrong medical diagnosis, error in a medical operation Palisade Risk Conference 2015, Mumbai 6
The Insurance Equation Setting a price for insurance Basic pricing formula for any product: Price = Cost + Profit For insurance, the equation becomes: Premium = Losses + Expenses + UW Profit The cost of production not known at time of sale Will the insured event(s) occur or not? Will there be multiple instances of occurrence? Will there be losses from multiple perils? What would be the extent of loss should the event(s) occur? Palisade Risk Conference 2015, Mumbai 7
Understanding the Insurance Equation Losses Policy sold Loss event occurs Claim notified to insurer Claim accepted by insurer Initial payment made, case reserve set Claim matures over time More payments made, case reserve adjusted Final payment made, claim closed Claim re-opened Claim finally settled and closed Ultimate loss from the claim now known More claims on the same policy notified at any stage above Same process for each claim till all claims on the policy are closed Ultimate Loss from the policy now known Palisade Risk Conference 2015, Mumbai 8
Understanding the Insurance Equation Expenses Loss Adjustment Expense (LAE) Expenses of handling and settling claims ALAE LAE = ALAE + ULAE ALAE = Allocated LAE Directly attributable to a specific claim Legal fee to defend a claim Medical costs, expert fee Underwriting Expense Expenses of acquiring and servicing policies Commissions and brokerage Any other acquisition costs; advertising Miscellaneous overheads for building maintenance ULAE ULAE = Unallocated LAE Cannot be assigned to a specific claim Salaries of the claims dept. General management costs Premium Taxes Palisade Risk Conference 2015, Mumbai 9
Understanding the Insurance Equation Underwriting Profit Cost of maintaining capital justifies an expected return on capital or a profit provision by the insurer UW Profit is equivalent to Income less Outgo from writing insurance policies Total Profit = UW Profit + Investment Income Investment Income from insurance funds and capital PLUS Underwriting profit......should sufficiently compensate the insurer for assuming risk Palisade Risk Conference 2015, Mumbai 10
Getting started... Collecting data Claims Data - Historical Loss Experience Dates Accident date, Report date, Settlement / Closure date Transaction date(s) Data as of date Amounts Paid loss, Case Reserve estimates Indemnity and expenses From ground-up; applicable deductible(s) Claim Status and Counts Reported / Open / Closed Loss details Claim type - disease, injury, damage Loss event description Identifiers Claim and Policy IDs Loss location - plant, subsidiary, unit Policy Data Policy details Inception and expiry dates Structure - limits, deductibles Terms of cover - claims made / occurrence Risks covered, exclusions Exposure measure details A measure indicative of risk within the policy Directly proportional to expected loss Payroll for Employers Liability Revenue for Public Liability Policy and Exposure data needed for both... Historical time period over which claims experience for the risk has been collected Future policy period for which premium is being projected Palisade Risk Conference 2015, Mumbai 11
Data considerations...and adjustments Accuracy Check for recording errors Compare to previous loss runs Adequacy Sufficient volume of data for a credible analysis Detailed enough to identify heterogeneity, if any Ample years of history to identify trends in claims and loss amounts Relevance Very old years of experience, though developed, may not be valid for the future Check for changes in Policy conditions, structure, coverage Underwriting standards Claims handling and settlement Any new or redundant risks? Acquisitions and disposals Entry in to or exit from certain markets Changed working procedures eliminating previously occurring loss events Make appropriate adjustments by excluding irrelevant data, smoothing out distortions caused by large or exceptional claims and create homogenous groups to price the risk Palisade Risk Conference 2015, Mumbai 12
Sample Claims data... Historical Claims Experience Palisade Risk Conference 2015, Mumbai 13
Sample Claims data......some questions to ask Reasonability checks... Any report dates before accident dates? Any close dates before report dates? Are accident dates falling within the policy period? Are all dates on or before the data as of date? Is claim status consistent with close dates? Any case reserves on closed claims? Single or multiple currencies? Create homogeneous groups to analyse separately, ensuring adequacy within each group... Separate EL and PL claims Separate bodily injury and property damage losses? Analyse fee and indemnity separately? Any specific loss location with very different loss experience? Any exceptionally large losses? Palisade Risk Conference 2015, Mumbai 14
Burning Cost Burning cost is the actual cost of claims expressed as an average loss per unit of exposure Also known as loss cost or pure premium Burning Cost = TotalLoss amount Exposure = Numberof Claims Exposure TotalLoss amount Numberof Claims = = Frequency Severity Claim incidence rate Average cost of claims Palisade Risk Conference 2015, Mumbai 15
Loss Development Taking reported loss to ultimate loss Data collected has Reported loss amounts on known claims Reported Loss = Paid Loss + Case Reserves Ultimate loss requires additional reserves for... development on known claims IBNER - incurred but not enough reported emergence and final settlement of new claims Pure IBNR - incurred but not reported Ultimate Loss = Reported Loss + IBNER + IBNR Palisade Risk Conference 2015, Mumbai 16
Loss Development Selecting a development pattern Aggregate data Triangulate Age-to-Age factor Age-to- Ultimate factor Percent Developed Palisade Risk Conference 2015, Mumbai 17
Developed Loss Severity Case development for IBNER IBNER is the estimated future development on case reserves currently held for reported open claims Review age-to-age development factors and select a development pattern for both loss amounts and number of claims Say, at 36 months of development, if 75% of losses are developed and 90% of claims have been reported, and......$150 of losses have been reported of which $70 are paid and the rest held in case reserves This implies an ultimate loss of $200 ( = 150 /.75 ) Since 90% of the claims have been reported, we take 90% of the total ultimate loss to be the ultimate loss on known claims i.e. $ 180 ( = 200 x.90 ) 70 Paid Loss 80 Case Reserves 150 Reported Loss 75% of losses are reported 200 Ultimate Loss 90% of the number of claims are reported 180 Ultimate Loss on known claims This implies the reported loss on known claims needs to go up from $150 to $180 as the ultimate loss on known claims Equivalently, case reserves need to go up from $80 to $110 i.e. up by a factor of 1.375 30 IBNER on known claims to take developed loss on known claims from 150 to 180 1.375 Case Development Factor for known claims to take case reserves on known claims from 80 to 110 110 / 80 = 1.375 Assuming the average severity of the risk on future reported claims is the same as that on the known claims Palisade Risk Conference 2015, Mumbai 18
Trending From historical to future time period Projecting historical losses to ultimate is not enough Losses further need to be projected to the cost level of the future period of cover for which premium is being estimated......for a period starting from the average date of loss occurrence in the historical experience to the mid-point of exposure from the future period of writing the policy Losses occuring from policies written in 2015 Losses occurring in 2013 Policies written in 2015 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 average date of loss occurrence in 2013 average date of loss occurrence based on accidents from policies written in 2015 2.5 years of loss trending Trends in frequency and severity need to be analysed separately and combined to get to the pure premium trend When exposure measures are subject to inflation, the frequency trend should be adjusted for trends in exposure Palisade Risk Conference 2015, Mumbai 19
Trended & Developed losses Aggregated sample data Select development patterns for reported loss amounts and number of claims Apply these to the client s data and estimate case development factors for developing known (open) claims to ultimate Select frequency, severity and exposure trends Trend the developed severity on known claims from their accident date to the average accident date in the future policy year i.e. from claim accident date to 30-Sep-15 in the above example Palisade Risk Conference 2015, Mumbai 20
Trended & Developed losses Detailed sample data by claim Select which historical years to include for fitting a loss severity distribution to For instance, the most recent year may be excluded on grounds of immaturity of experience Palisade Risk Conference 2015, Mumbai 21
@Risk for distribution fitting...to selected T&D claims Palisade Risk Conference 2015, Mumbai 22
Goodness of fit QQ plot; CDF from fit The fit could be improved by considering different distributions for smaller losses, in this case below $1,000 Say, the policy structure being priced requires a per claim limit of $1Mn. Largest T&D loss point from the historical experience is $112,944. No losses in the experience of the past 7 years exceeding $150K. Do we give $150K to $1Mn for free?!? Fit a Pareto curve to the tail distribution; Price the tail using increased limit factors Slice the selected T&D loss points into different sized layers and re-fit distributions to each layer Palisade Risk Conference 2015, Mumbai 23
@Risk for distribution fitting...to selected T&D claims by layers Palisade Risk Conference 2015, Mumbai 24
Combined Severity Distribution RiskSplice function Fitted Weibull distribution for loss size 0 to 1,000 spliced with fitted LogNormal for size 1,000 to 25,000 at splice point 1,000 Resulting distribution spliced with a Pareto fitted tail distribution above 25,000 Palisade Risk Conference 2015, Mumbai 25
Trended & Developed frequency Aggregated sample data Trend and develop number of claims using the select development pattern and trend factors Adjust to bring them to levels of future policy period s estimated exposure Select years to include and choose a frequency distribution e.g. Poisson or Negative Binomial Parameterise the frequency distribution Palisade Risk Conference 2015, Mumbai 26
Simulating loss cost Compound distribution Use the RiskCompound function and simulate to generate mean loss cost... From ground-up, limited to policy limit Within deductible layer Within insured layer Higher percentiles may be reviewed to see the extent of variability in any layer; for instance to choose an annual aggregate deductible (AAD) at a level comfortable of not being breached Use the RiskSimTable to run results of the same simulation through multiple sets of layers; for instance, to price more complex structures involving non-ranking deductibles that do not erode the AAD Palisade Risk Conference 2015, Mumbai 27
Summary of results Palisade Risk Conference 2015, Mumbai 28
Premium Add to the selected loss cost for the insured layer... Allowance for expenses Profit load Any load for losses not modelled Large losses Latent claims Disease claims Catastrophe losses Allowance for reinsurance...to get to the premium to charge for the cover And hope we ve got it right! Palisade Risk Conference 2015, Mumbai 29
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