Grossi - CAT2 Flashcards
models can output expected losses but they can also output
exceedance probability curves
3 types of exceedance probability curves
- Occurrence exceedance probability
- probability that loss for at least 1 event exceeds specified loss amount during a given time period
- useful to insurer interested in buying per occurrence XOL - aggregate exceedance probability
- probability that sum of all losses exceeds specified loss amount during a given time period
- useful to insurer interested in buying aggregate reinsurance - conditional exceedance probability
- probability that amount on single event exceeds a specified loss amount given that the event occurs
- useful to insurer in setting reserves after event occurs
tail of graph gets most attention
it may contain events that could potentially bankrupt the company
tail should drop to 0 probabiltiy around where losses are = total IV
based on graph of exceedance probability
insurers can decide what level of risk is tolerable and make risk management decisions to deal with unacceptable levels of risk
in general, there are 2 conditions for insurer to be willing to provide coverage to a risk:
- ability to identify and quantify probability of event and severity of loss
- ability to set premiums for each customer
because risk is insurable, doesn’t mean
its profitable so insurer needs to charge rate that is both profitable and produces adequate demand (ie affordable)
considerations in setting rates for CAT events
State regulations
Competition
Uncertainty of losses
Highly correlated losses (CAT losses are not independent; do not follow law of large #s, single event can produce significant losses)
Adverse selection
Moral hazard
Liquidity of assets (liquid assets produce lower returns so need to charge higher premium to reflect this opportunity cost)
4 ratemaking principles
CAT models help devise rates that follow them:
- rate is estimate of expected value of future costs
- rate provides for all costs associated with transfer of risk
- rate provides for costs associated with individual risk transfer
- rate is reasonable and not excessive, inadequate, or unfairly discriminatory if it is actuarially sound estimate of expected value of all future costs associated with individual risk transfer
cat model can help determine both
the AAL and risk load
model can help determine equitable AAL for different risks based on
- structure attributes: these relate to physical performance of building during a cat (construction type, occupnacy type, building codes, construction yr)
- location attributes: these relate to proximity and susceptibility to hazard of building (distance from fault lines, distance from coast, soil type)
regulators have historically not been supportive of use of cat models in ratemaking because
- it is difficult for regulators to evaluate modes since they require subject matter experts
- modeling firms are unwilling to share key proprietary elements of their models especially in states that require government documents to be publicly available
- models present a conflict for regulators since they present a scientifically rational approach to quantifying potential risk but models could also be used by insurers as justification for charging higher rates
- note there are some publicly available cat models that can be used by regulators to compare with models created by private companies
CA EQ authority
- formed after Northridge EQ caused billions of damage
- insurers were threatening to leave market due to loss potential
- CA created CEA as publicly managed insurer for EQ risk
- given contraints of: rates needed to be actuarially sound and if scientific info was used in RMing, it should be consistent with available geophysical data and current knowledge of scientific community
- initial rates were based on CAT models and were immediately challenged by consumer groups
potential problems with using catastrophe models for ratemaking.
- Model to model variance - the same input could produce very different results if another model is used.
- Public acceptance - the public has been slow to accept the models since they generally result in higher rates.
- Regulators have not widely accepted the use of models. It requires expertise to evaluate,modeling firms don’t release all proprietary aspects of models, and they often result in rate increases.
- They lie outside most actuaries’ expertise.
actuarial acceptance
important for actuaries to become familiar with componetns of model because models lie outsde of usual actuarial expertise
-ASB requires:
determine appropriate reliance on experts
have a basic understanding of model
evaluate whether model is appropriate for intended use
determine approproate validation has occurred
determine appropraite use of model
2 types of uncertainty related to cat models
- aleatory - inherent randomness associated with natural hazard events; usually reflected in probability distributions; cat version of proces risk
-
epistemic - uncertainty due to lack of knowledge of hazard; cat version of parameter risk
- modelers due need to make sure they do not ignore or double count uncertainties
epistemic uncertainty comes about
- limited scientific knowledge
- limited historical data
- cross disciplinary nature of cat models: involve interaction of experts from different functions
- lack of data to create geographic information system databases
- lack of accurate data on true market values
- lab testing of structural material has been limited to certain tpes of materials; limited understanding of how other materials perform
2 main ways to incorporate uncertainty into cat models
- logic trees
- simulation techniques
logic trees
- displays alternative parameter values or mathematical relationships along with associated weights for each alternative
- alternatives are weighted together to produce estimates for each parameter or relationship
- advantages: tractability, usefulness as tool to communicate risk
- disadvantages: weights are often based on expert opinion and may be biased
simulation techniques
- simulation can be used to model a real system by building a model that attempts to replicate system’s behavior
- can be used to handle more complicated scenarios than logic trees can handle and can be sued to derive probability distributions
- unlike logic trees, can be used for both discrete and continuous distributions
can also use exceedance probability curves using a combo of logic trees and simulation
- under this method, each brand of logic tree represents alternative that samples from a probability distribution using a simulation
- each branch can generate its own EP curve
- can calculate a mean, median, and Cis for a combined EP curve using curves for different branches
- similar to concept of combining EP curves from different branches of logic tree within same model is concept of combining EP curves from different models
- model users deal with uncertainty of modeling by weighting together outputs of multiple models
3 special issues insurers need to account for in managing their portfolio risk
- data quality
- insurers need to make sure their data is sued in inventory module is accurate
- increasing data quality can reduce epistemic uncertainty
- particularly true for important variables like construction type or age of building - uncertainty modeling
- losses should not be allocated to stakeholders based solely on expected value but instead based on probability distributions - impact of correlation
- having a more diversified portfolio reduces risk of single event resulting in damages to large portion of portfolio
residential v commerical policies
- residential policies have single location with limits by coverage and usually a single deductible; insurer should have moderately detailed data about properties
- commercial policies may have buildings in multiple locations covered by the same policy; each building would usually have high replacement cost and there may be limits and deductibles that vary by location in addition to policy level limits and deductibles; given larger amount of risk, insurer should have highly detailed data about these properties
when deciding whether or not to add a new policy to portfolio, underwriters should consider
Magnitude of risk
Correlation with existing portfolio
Highest price that risk is willing to pay
-cat models help make decision more objective by quantifying risk posed
Bottom up approach to portfolio modeling
- following steps:
1. model losses at location level
2. aggregate losses across all locations for each policy
3. aggregate losses across all policies for each portfolio
4. if insurer has multiple portfolios, aggregate losses across portfolios - instead of aggregating losses for entire portfolio, insurers can also aggregate losses by zip code
- can use this work to identify high risk zip codes for which they might want to limit their exposure, possibly by curtailing new business
- losses by stakeholder can be visualized with loss diagrams
in case with multiple portfolios
diversification across portfolios reduces impact of individual events to insurer
company has decided to minimize risk. Explain which portfolio the insurer should
eliminate.
Looking at the portfolios, you can visually see that portfolios 1 and 3 are positively correlated and both are negatively correlated with portfolio 2. To increase diversification, we should eliminate either portfolio 1 or 3. Since the standard deviation is higher for portfolio 3 than for portfolio 1, we should eliminate portfolio 3.
exceedance probability curve represents.
An exceedance probability curve shows all possible levels of loss and the probability that the loss level will be exceeded in a given period of time. An occurrence EP curve shows the probability that at least 1 loss will exceed the loss level, while an aggregate EP curve shows the probability that the sum of all losses will exceed the loss level.
common uses for exceedance probability curves.
• Calculate the PML for a given payout period.
• Calculate if the portfolio meets a solvency goal.
• Decide what proportion of risks should be ceded to reinsurers.
• Used to calculate average annual loss.
• Set level of conservativeness, such as PML in 1/X chance.
• Used to find a strategy to change the portfolio if it is currently above the level of
conservativeness.
• Used by emergency response units to determine where damage might be and build strategies in times of catastrophes.
• Used when running logic trees. Instead of using point estimates, each branch of the tree can have its own exceedance probability curve for the different outcomes, which can then be combined.
• Emergency management services can use them to evaluate the potential risk of some regions and plan evacuations.
• Reinsurance brokers can use them to evaluate the level of risk in their portfolios and estimate the impact of accepting new risks.
