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CAS CARe SeminarBaltimore, June 1999G(%OverviewRisks faced by an (re-)insurer (JB)
Need for aggregate loss distributions (SM)
Measures of risk (SM)
Creating aggregate distributions (SM)
Strategy Design and Implementation (JB)2Risks Faced by InsurersrLowe & Stanard (Spring 1996 Forum) risks faced by an insurance enterprise
Liability Risk
Asset Risk
Business Risk
6J(J($cCRisks Faced by InsurersFUnderwriting Risk
Balance Sheet Risk
Business Risk
Organizational Risk3Aggregate Loss DistributionsAnalysis of risks shows understanding of liabilities is key
Insurance liabilities variable in amount and timing
Initial focus is on amount of loss
Suggests an accident year ultimate view
Future work to consider timing risk (see my upcoming DFA Seminar talk in Chicago)$zz4Aggregate Loss DistributionsDesign criteria for producing aggregates
Include all lines of business, all liabilities
Appropriate treatment of catastrophes
Capture correlation
Within year, between line
Between years6)i()i(5Aggregate Loss DistributionsAll lines of business
Total risk management program must take portfolio view
Achieving balance at department / business unit levels expensive and serves no economic purpose
Risk fundamentally a question of aggregationH7`-7`-:
Aggregate Loss DistributionsVAll lines of business
Effect of adding uncorrelated risk on extreme percentiles is less than expected, especially after considering pricing
Example: Expected loss ratio 80% on $375M premium, losses lognormal with CV 0.20
99%ile loss ratio is 124%
Add ILW type loss, 5% chance of $50M payout, 95% chance of $0M payout, priced at 50% loss ratio6vvBAggregate Loss DistributionsExample continued
ILW premium is $2.5M / 0.5 = $5.0M
99%ile losses increase by only $4.8M to $471M
99%ile loss ratio unchanged at 124%
Shows combined effect of adding lower loss ratio business and portfolio effect on losses
Computation is based on conditional probability:P(L+SMeasures of Risk1Stability is desire for actual results to be reasonably close to plan
Possible measures include variance, standard deviation, CV, down-side risk
Percentile related measures more direct
9 years out of 10, combined ratio should be between plan + x and plan + y
Lower bound is guide to suitable risk appetiteRy ;/?Measures of RiskbGraphic illustrates constraints
Stability is horizontal constraint
Solvency is vertical constraint0 C B8%Creating Aggregate Loss DistributionsMany tools available for making aggregates
See other sessions at CARe!
Frequency and severity approach
Stratify book by attachment and limit
Model cats separately
Method of moments to match three moments for large books6++A@%Creating Aggregate Loss DistributionsFast Fourier Transform methods
Programming overhead to set up
S. Wang Proceedings paper (www.casact.org)
Simulation too slow
Recursive methods more of academic interest and very computationally intensive6JcJc]iA%Creating Aggregate Loss DistributionsCorrelation between lines: use Iman-Conover shuffling method or other copula based method
Again, see Wang s paper
Gives sample from multivariate distribution with desired correlation structure
Easy to implement
Can be done in Excel
Basis for correlations in At Risk$ZZ,<Strategy DesignGOAL: Maximize profit objective subject to risk constraints
Requires quantifiable measures of risk
Requires targets for risk constraints
Requires structuring risk management program to meet targets
Requires monitoring of performance against targetsl== 1
!DStrategy DesignQuantifiable Measures of Risk
Solvency Measures
Probability of Ruin
Probability of Impairment
Probability of Employment
Stability Measures
Probability of Combined Ratio > x%
Probability of Exceeding Plan by y%
Probability of Under Performing the Market by z%ZHxHxEStrategy DesignxEstablishing Targets
Structuring Risk Management Program
Mix of Business
Net Retained Lines
Reinsurance!
Implementation
69090FImplementationUse of Reinsurance
Have a defined purpose for reinsurance
Promote Stability
Promote Solvency
There are other uses for reinsurance
Evaluate the benefit provided versus the cost
Continue to Monitor performance against expectationsH'Hc'Hc/TIPb ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,v?Kd@ @A@` n?" dd@ @@``PR @ ` `p>><4( --NNNppp
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we are future management
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g4%d%d`b0Xb Bp@pp?%y"=The Role of Reinsurance in a Total Risk Management Program >><FJohn BeckmanStephen Mildenhall
CAS CARe SeminarBaltimore, June 1999G(%OverviewRisks faced by an (re-)insurer (JB)
Need for aggregate loss distributions (SM)
Measures of risk (SM)
Creating aggregate distributions (SM)
Strategy design and implementation (JB)2Risks Faced by InsurersrLowe & Stanard (Spring 1996 Forum) risks faced by an insurance enterprise
Liability Risk
Asset Risk
Business Risk
6J(J($cCRisks Faced by InsurersFUnderwriting Risk
Balance Sheet Risk
Business Risk
Organizational Risk3Aggregate Loss DistributionsAnalysis of risks shows understanding of liabilities is key
Insurance liabilities variable in amount and timing
Initial focus is on amount of loss
Suggests an accident year ultimate view
Future work to consider timing risk (see my upcoming DFA Seminar talk in Chicago)$zz4Aggregate Loss DistributionsDesign criteria for producing aggregates
Include all lines of business, all liabilities
Appropriate treatment of catastrophes
Capture correlation
Within year, between line
Between years6)i()i(5Aggregate Loss DistributionsAll lines of business
Total risk management program must take portfolio view
Achieving balance at department / business unit levels expensive and serves no economic purpose
Risk fundamentally a question of aggregationH7`-7`-:
Aggregate Loss DistributionsVAll lines of business
Effect of adding uncorrelated risk on extreme percentiles is less than expected, especially after considering pricing
Example: Expected loss ratio 80% on $375M premium, losses lognormal with CV 0.20
99%ile loss ratio is 124%
Add ILW type loss, 5% chance of $50M payout, 95% chance of $0M payout, priced at 50% loss ratio6vvBAggregate Loss DistributionsExample continued
ILW premium is $2.5M / 0.5 = $5.0M
99%ile losses increase by only $4.8M to $471M
99%ile loss ratio unchanged at 124%
Shows combined effect of adding lower loss ratio business and portfolio effect on losses
Computation is based on conditional probability:P(L+S><FJohn BeckmanStephen Mildenhall
CAS CARe SeminarBaltimore, June 1999G(%OverviewRisks faced by an (re-)insurer (JB)
Need for aggregate loss distributions (SM)
Measures of risk (SM)
Creating aggregate distributions (SM)
Strategy design and implementation (JB)2Risks Faced by InsurersrLowe & Stanard (Spring 1996 Forum) risks faced by an insurance enterprise
Liability Risk
Asset Risk
Business Risk
6J(J($cCRisks Faced by InsurersFUnderwriting Risk
Balance Sheet Risk
Business Risk
Organizational Risk3Aggregate Loss DistributionsAnalysis of risks shows understanding of liabilities is key
Insurance liabilities variable in amount and timing
Initial focus is on amount of loss
Suggests an accident year ultimate view
Future work to consider timing risk (see my upcoming DFA Seminar talk in Chicago)$zz4Aggregate Loss DistributionsDesign criteria for producing aggregates
Include all lines of business, all liabilities
Appropriate treatment of catastrophes
Capture correlation
Within year, between line
Between years6)i()i(5Aggregate Loss DistributionsAll lines of business
Total risk managem6 Aggregate Loss DistributionsCatastrophes
Major source of variability in liabilities
Major source of correlation between lines of business
Sophisticated models available to quantify amount and distribution of losses
Recommend modeling cat losses separately from non-cat losses$
;Aggregate Loss Distributions8Capture correlation
Cat, discussed above
Non-cat correlations in loss ratios largely driven by pricing (year-to-year) and property
Beware statewide splits of data which introduce hard-to-model correlations
One-year accident year plans can incorporate common pricing movements
Allows realistic model of loss ratioloKkKKk=Measures of Risk"Risk management process requires quantifiable measures of risk and setting targets for risk constraints
Measures should capture solvency and stability constraints
Solvency is related to probability of loss in excess of a key threshold, such as comb-ined ratio which would trigger down-gradel#6-
x&>Measures of Risk1Stability is desire for actual results to be reasonably close to plan
Possible measures include variance, standard deviation, CV, down-side risk
Percentile related measures more direct
9 years out of 10, combined ratio should be between plan + x and plan + y
Lower bound is guide to suitable risk appetiteRy ;/?Measures of RiskbGraphic illustrates constraints
Stability is horizontal constraint
Solvency is vertical constraint0 C B8%Creating Aggregate Loss DistributionsMany tools available for making aggregates
See other sessions at CARe!
Frequency and severity approach
Stratify book by attachment and limit
Model cats separately
Method of moments to match three moments for large books6++A@%Creating Aggregate Loss DistributionsFast Fourier Transform methods
Programming overhead to set up
S. Wang Proceedings paper (www.casact.org)
Simulation too slow
Recursive methods more of academic interest and very computationally intensive6JcJc]iA%Creating Aggregate Loss DistributionsCorrelation between lines: use Iman-Conover shuffling method or other copula based method
Again, see Wang s paper
Gives sample from multivariate distribution with desired correlation structure
Easy to implement
Can be done in Excel
Basis for correlations in At Risk$ZZ,<Strategy DesignGOAL: Maximize profit objective subject to risk constraints
Requires quantifiable measures of risk
Requires targets for risk constraints
Requires structuring risk management program to meet targets
Requires monitoring of performance against targetsl== 1
!DStrategy DesignQuantifiable Measures of Risk
Solvency Measures
Probability of Ruin
Probability of Impairment
Probability of Employment
Stability Measures
Probability of Combined Ratio > x%
Probability of Exceeding Plan by y%
Probability of Under Performing the Market by z%ZHxHxEStrategy DesignxEstablishing Targets
Structuring Risk Management Program
Mix of Business
Net Retained Lines
Reinsurance!
Implementation
69090FImplementationUse of Reinsurance
Have a defined purpose for reinsurance
Promote Stability
Promote Solvency
There are other uses for reinsurance
Evaluate the benefit provided versus the cost
Continue to monitor performance against expectationsH'Hc'Hc/TIPb6
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_PID_GUIDAN{93592200-18D1-11D3-9CCE-0004ACBA2083}ent program must take portfolio view
Achieving balance at department / business unit levels expensive and serves no economic purpose
Risk fundamentally a question of aggregationH7`-7`-:
Aggregate Loss DistributionsVAll lines of business
Effect of adding uncorrelated risk on extreme percentiles is less than expected, especially after considering pricing
Example: Expected loss ratio 80% on $375M premium, losses lognormal with CV 0.20
99%ile loss ratio is 124%
Add ILW type loss, 5% chance of $50M payout, 95% chance of $0M payout, priced at 50% loss ratio6vvBAggregate Loss DistributionsExample continued
ILW premium is $2.5M / 0.5 = $5.0M
99%ile losses increase by only $4.8M to $471M
99%ile loss ratio unchanged at 124%
Shows combined effect of adding lower loss ratio business and portfolio effect on losses
Computation is based on conditional probability:P(L+SMeasures of Risk1Stability is desire for actual results to be reasonably close to plan
Possible measures include variance, standard deviation, CV, down-side risk
Percentile related measures more direct
9 years out of 10, combined ratio should be between plan + x and plan + y
Lower bound is guide to suitable risk appetiteRy ;/?Measures of RiskbGraphic illustrates constraints
Stability is horizontal constraint
Solvency is vertical constraint0 C B8%Creating Aggregate Loss DistributionsMany tools available for making aggregates
See other sessions at CARe!
Frequency and severity approach
Stratify book by attachment and limit
Model cats separately
Method of moments to match three moments for large books6++A@%Creating Aggregate Loss DistributionsFast Fourier Transform methods
Programming overhead to set up
S. Wang Proceedings paper (www.casact.org)
Simulation too slow
Recursive methods more of academic interest and very computationally intensive6JcJc]iA%Creating Aggregate Loss DistributionsCorrelation between lines: use Iman-Conover shuffling method or other copula based method
Again, see Wang s paper
Gives sample from multivariate distribution with desired correlation structure
Easy to implement
Can be done in Excel
Basis for correlations in At Risk$ZZ,<Strategy DesignGOAL: Maximize profit objective subject to risk constraints
Requires quantifiable measures of risk
Requires targets for risk constraints
Requires structuring risk management program to meet targets
Requires monitoring of performance against targetsl== 1
!DStrategy DesignQuantifiable Measures of Risk
Solvency Measures
Probability of Ruin
Probability of Impairment
Probability of Employment
Stability Measures
Probability of Combined Ratio > x%
Probability of Exceeding Plan by y%
Probability of Under Performing the Market by z%ZHxHxEStrategy DesignxEstablishing Targets
Structuring Risk Management Program
Mix of Business
Net Retained Lines
Reinsurance!
Implementation
69090FImplementationUse of Reinsurance
Have a defined purpose for reinsurance
Promote Stability
Promote Solvency
There are other uses for reinsurance
Evaluate the benefit provided versus the cost
Continue to monitor performance against expectationsH'Hc'HcJReinsurance vs. Capital Markets Reinsurance Securitization
Risk Matching Tailored Standardized
Accounting Reinsurance Varies/Complex
Trans. Expense Low High
Price ?? ??!8oo/TIPb
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sparkles.ppt>The Role of Reinsurance iJB)
Need for aggregate loss distributions (SM)
Measures of risk (SM)
Creating aggregate distributions (SM)
Strategy design and implementation (JB)2Risks Faced by InsurersrLowe & Stanard (Spring 1996 Forum) risks faced by an insurance enterprise
Liability Risk
Asset Risk
Business Risk
6J(J($cCRisks Faced by InsurersFUnderwriting Risk
Balance Sheet Risk
Business Risk
Organizational Risk3Aggregate Loss DistributionsAnalysis of risks shows understanding of liabilities is key
Insurance liabilities variable in amount and timing
Initial focus is on amount of loss
Suggests an accident year ultimate view
Future work to consider timing risk (see my upcoming DFA Seminar talk in Chicago)$zz4Aggregate Loss DistributionsDesign criteria for producing aggregates
Include all lines of business, all liabilities
Appropriate treatment of catastrophes
Capture correlation
Within year, between line
Between years6)i()i(5Aggregate Loss DistributionsAll lines of business
Total risk management program must take portfolio view
Achieving balance at department / business unit levels expensive and serves no economic purpose
Risk fundamentally a question of aggregationH7`-7`-:
Aggregate Loss DistributionsVAll lines of business
Effect of adding uncorrelated risk on extreme percentiles is less than expected, especially after considering pricing
Example: Expected loss ratio 80% on $375M premium, losses lognormal with CV 0.20
99%ile loss ratio is 124%
Add ILW type loss, 5% chance of $50M payout, 95% chance of $0M payout, priced at 50% loss ratio6vvBAggregate Loss DistributionsExample continued
ILW premium is $2.5M / 0.5 = $5.0M
99%ile losses increase by only $4.8M to $471M
99%ile loss ratio unchanged at 124%
Shows combined effect of adding lower loss ratio business and portfolio effect on losses
Computation is based on conditional probability:P(L+SMeasures of Risk0Stability is desire for actual results to be reasonably close to plan
Possible measures include variance, standard deviation, CV, down-side risk
Percentile related measures more direct
1 year out of 10, combined ratio should be between plan + x and plan + y
Lower bound is guide to suitable risk appetiteRx :/?Measures of RiskbGraphic illustrates constraints
Stability is horizontal constraint
Solvency is vertical constraint0 C B8%Creating Aggregate Loss DistributionsMany tools available for making aggregates
See other sessions at CARe!
Frequency and severity approach
Stratify book by attachment and limit
Model cats separately
Method of moments to match three moments for large books6++A@%Creating Aggregate Loss DistributionsFast Fourier Transform methods
Programming overhead to set up
S. Wang Proceedings paper (www.casact.org)
Simulation too slow
Recursive methods more of academic interest and very computationally intensive6JcJc]iA%Creating Aggregate Loss DistributionsCorrelation between lines: use Iman-Conover shuffling method or other copula based method
Again, see Wang s paper
Gives sample from multivariate distribution with desired correlation structure
Easy to implement
Can be done in Excel
Basis for correlations in At Risk$ZZ,<Strategy DesignGOAL: Maximize profit objective subject to risk constraints
Requires quantifiable measures of risk
Requires targets for risk constraints
Requires structuring risk management program to meet targets
Requires monitoring of performance against targetsl== 1
!DStrategy DesignQuantifiable Measures of Risk
Solvency Measures
Probability of Ruin
Probability of Impairment
Probability of Employment
Stability Measures
Probability of Combined Ratio > x%
Probability of Exceeding Plan by y%
Probability of Under Performing the Market by z%ZHxHxEStrategy DesignxEstablishing Targets
Structuring Risk Management Program
Mix of Business
Net Retained Lines
Reinsurance!
Implementation
69090FImplementationUse of Reinsurance
Have a defined purpose for reinsurance
Promote Stability
Promote Solvency
There are other uses for reinsurance
Evaluate the benefit provided versus the cost
Continue to monitor performance against expectationsH'Hc'HcJReinsurance vs. Capital Markets Reinsurance Securitization
Risk Matching Tailored Standardized
Accounting Reinsurance Varies/Complex
Trans. Expense Low High
Price ?? ??!8oo/TIPbr'p0Jb