C.01.Grossi
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4 components of catastrophe models
 hazard: produces the parameters of the catastrophe
 inventory: pf info (location, construction type, age, ...)
 vulnerability: susceptibility of the properties to damage
 loss: generates $ loss (direct & indirect)

Parties interested by catastrophe models
 insurer & reinsurer
 reinsurer broker (assess client risk)
 capital mkt (catrelated products)
 regulators
 emergency mgt agencies (coordinate emergency response)

Exceedance Probability (EP) curve
 indicates probability that a specific loss level will be surpassed during a given period
 insurers can use it to decide how much risk to transfer

EP formulas
 assume only 1 loss can occur annually
 EP(L_{i}) = p(L≥L_{i}) = 1  p(L≤L_{i}) = 1  Π(1p_{i})
 Average Annual Loss = AAL = Σp_{i}L_{i}

Probable Maximum Loss (PML)
Loss associated with a given low probability level

Segmenting EP curve
 general case: 3 parties involved = insd (ded), insr (lim), reinsr
 each has its own EP curve allocated
 each can decide how to price, how much covg needed, ...

2 criterias for an insr to provide covg
 ability to identify & quantify event prob & loss severity
 ability to set premiums for each potential customer

Factors to consider when determining premium
 balance btwn profitability & demand
 state regulation
 competition
 uncertainty of losses
 loss correlation
 adverse selection
 moral hazard

Determining whether to provide coverage
 insr wants prob of insolvency to be less than p_{1}
 assume each prop has prem Z, surplus A
 if p(loss > n * Z + A) < p_{1} we can keep growing

Regular statistical tools vs cat modeling
 often inappropriate
 insufficient claim data
 limited avail data usually inappropriate due to changing factors

Hazard model main parameters
 location
 frequency
 severity
 historic data can only be used for initial prob dist

Inventory model
 most of the data comes from governmt
 data includes # prop & value by LOB / Occupancy / Covg / Construction Type
 insr may incorporate more riskspecific info
 identify missing & erroneous data, test for reasonability

Vulnerability model
 estimate damage to properties
 engineering judgment: (+) simpler () arbitrary () hard to update
 building response analyses based on advanced engineering techniques (+) more accurate () inappropriate for assessment of entire pf (tailored towards specific buildg)
 tweak prev method: split pf into classes; identify typical buildg; evaluate buildg performance (damage fctn) (damage ratio = repair cost / replacement)

Loss model
 link parameters of the event directly into $ (opinion based) (+) more straightforward () hard to update
 determine physical damage from event & use engineering to convert to $
 finally derive insd loss considering limits / ded / coins / ...

2 types of cat model uncertainty
 Aleatory: inherent randomness associated w natural hazard events. Usually reflected in prob dist
 Epistemic: due to lack of info / knowledge of hazard
 not necessary to distinguish, make sure not ignored or double counted

Sources of epistemic uncertainty
 limited scientific knowledge
 limited historic data
 crossdisciplinary nature of cat (seism, meteo, engineer)
 lack of data to create GIS database
 limited laboratory testing on certain types of materials

2 methods to incorporate uncertainty
 logic tree: displays param or math relationship along w weights (+) tractability & usefulness to communicate risk
 simulation techniques: can be used for more complex scenarios or to derive prob dist (+) more accurate

Insurance vs catastrophic losses
 losses from hazards are highly correlated
 insr need to maintain sufficient liquid assets → reflect opportunity cost in P

4 principles that determine whether a rate is actuarially sound, reasonable and not unfairly discriminatory
 a rate needs to be an estimate of the expected value of future costs
 a rate provides for all costs associated with the transfer of risk
 a rate provides for the cost associated w indiv risk transfer
 a rate is reasonable & not excessive, adequate, or not unfairly discriminatory if it is an actuarially sound estimate of the exp value of all future costs associated w individual risk transfer

Simple ratemaking model
 P = AAL + Risk load + Expense Load
 risk load depends on the uncertainty on AAL

2 most important cat model factors to diff btwn risks
 structure attribute of a pf (inventory cpnts) determine physical performance of building
 location attribute (proximity / succeptibility to hazard)

Regulation & cat modeling
 can use cat modeling to help educate regulators
 regulators historically not supportive since (1) requires expertise and (2) modeling firms want to protect proprietary info
 (+) provides scientifically rational approach
 () can be used to justify rate increase

Case study: California EQ Authority (CEA)
 formed after insr concerned w EQ threatened to leave mkt
 2 rate constraints: actuarially sound, scientific info consistent w avail geophysical data & current knowledge

Major issues w CEA model
 EQ recurrence rates: more than twice historical record
 uncertainty around time dependant probabilities
 damage curve based mainly on Northridge EQ
 model loss = % of bldg value → understated if val < replacmt
 diff to determine degree of demand surge
 model can't account for CEA policy features

Open issues on cat model
 regulatory acceptance: no technical expertise
 public acceptance: low because results in higher rates
 actuarial acceptance: lie outside of actuary's usual experise but ASB requires reliance on experts; basic understanding; determine appropriate use of model
 model to model variance: often significant btwn models

Pf composition
 Residential: simple structure. Covers bldg, ctnt, living exp. Insr has detailed data
 Commercial: may have several loc w high replacemt cost, need for highly detailed data

Factors to consider when deciding whether to add account to pf
 magnitude of the risk
 correlation w existing pf
 highest price the risk is willing to pay
 cat model = transparent method of evaluating impact of new risk

Cat modeling: bottomup approach
 calculate loss for insd & insr at the location lvl
 aggregate all locations losses by policy
 aggregate all losses
 all steps based on current pf

2 critical questions when facing cat risk
 what is AAL
 what's the likelihood that the insr would go insolvent → need a good model for right EP tail

Special issues regarding pf risk
 data quality: need to ensure it's accurate to reduce epistemic uncertainty
 uncertainty modeling: losses should not be allocated to parties based solely on exp value
 impact of correlation: impacts amt of diversification