Grossi - CAT2

Question 1

models can output expected losses but they can also output

Answer 1

exceedance probability curves

Question 2

3 types of exceedance probability curves

Answer 2

1. 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
2. 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
3. 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

Question 3

tail of graph gets most attention

Answer 3

it may contain events that could potentially bankrupt the company

tail should drop to 0 probabiltiy around where losses are = total IV

Question 4

based on graph of exceedance probability

Answer 4

insurers can decide what level of risk is tolerable and make risk management decisions to deal with unacceptable levels of risk

Question 5

in general, there are 2 conditions for insurer to be willing to provide coverage to a risk:

Answer 5

1. ability to identify and quantify probability of event and severity of loss
2. ability to set premiums for each customer

Question 6

because risk is insurable, doesn’t mean

Answer 6

its profitable so insurer needs to charge rate that is both profitable and produces adequate demand (ie affordable)

Question 7

considerations in setting rates for CAT events

Answer 7

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)

Question 8

4 ratemaking principles

Answer 8

CAT models help devise rates that follow them:

1. rate is estimate of expected value of future costs
2. rate provides for all costs associated with transfer of risk
3. rate provides for costs associated with individual risk transfer
4. 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

Question 9

cat model can help determine both

Answer 9

the AAL and risk load

Question 10

model can help determine equitable AAL for different risks based on

Answer 10

1. structure attributes: these relate to physical performance of building during a cat (construction type, occupnacy type, building codes, construction yr)
2. location attributes: these relate to proximity and susceptibility to hazard of building (distance from fault lines, distance from coast, soil type)

Question 11

regulators have historically not been supportive of use of cat models in ratemaking because

Answer 11

1. it is difficult for regulators to evaluate modes since they require subject matter experts
2. 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

Question 12

CA EQ authority

Answer 12

• 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

Question 13

potential problems with using catastrophe models for ratemaking.

Answer 13

• 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.

Question 14

actuarial acceptance

Answer 14

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

Question 15

2 types of uncertainty related to cat models

Answer 15

1. aleatory - inherent randomness associated with natural hazard events; usually reflected in probability distributions; cat version of proces risk
2. 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

Question 16

epistemic uncertainty comes about

Answer 16

• 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

Question 17

2 main ways to incorporate uncertainty into cat models

Answer 17

1. logic trees
2. simulation techniques

Question 18

logic trees

Answer 18

• 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

Question 19

simulation techniques

Answer 19

• 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

Question 20

can also use exceedance probability curves using a combo of logic trees and simulation

Answer 20

• 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

Question 21

3 special issues insurers need to account for in managing their portfolio risk

Answer 21

1. 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
2. uncertainty modeling
   - losses should not be allocated to stakeholders based solely on expected value but instead based on probability distributions
3. impact of correlation
   - having a more diversified portfolio reduces risk of single event resulting in damages to large portion of portfolio

Question 22

residential v commerical policies

Answer 22

• 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

Question 23

when deciding whether or not to add a new policy to portfolio, underwriters should consider

Answer 23

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

Question 24

Bottom up approach to portfolio modeling

Answer 24

• 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

Question 25

in case with multiple portfolios

Answer 25

diversification across portfolios reduces impact of individual events to insurer

Question 26

company has decided to minimize risk. Explain which portfolio the insurer should
eliminate.

Answer 26

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.

Question 27

exceedance probability curve represents.

Answer 27

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.

Question 28

common uses for exceedance probability curves.

Answer 28

• 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.