Clark - reinsurance2

Question 1

Inuring Reinsurance

Answer 1

• in case excess treaty applies on top of another reinsurance such as surplus share, some adjustments need to be made to price for treaty
• for experience rating, need to restate historical experience to be net of inuring reinsurance
• exposure rating can be applied directly to adjusted risk profile that is adjusted for inuring reinsurance
• if exposure curves vary by risk size, select curve based on gross insured value but apply exposure factors to expected losses net of inuring reinsurance

Question 2

casualty per occurrence XL treaties are usually separated into 3 layers

Answer 2

1. working layer – lower layer that is expected to be hit
2. exposed layer – higher layer but attaches below some underlying policy limits; layer is hit less frequently and may not be hit at all in some years
3. clash covers – high layer that is usually only hit due to multiple policies involving a single occurrence; could also be hit by extra contractual obligations or rulings awarding damages in excess of policy limits; layer could also be hit by a single policy is alae is included in treaty

Question 3

alae treated in 1 of 2 ways

Answer 3

1. included with loss – sum up loss and alae and treat as single amount when comparing to limit and retention
2. pro-rata with loss – calculate portion of ground up loss covered by treaty; same percentage of ground-up alae will also be covered

(neither favor one party or other)

Question 4

Clark suggestions for GL and AL severity curves

Answer 4

Pareto and mixed exponential distributions

Question 5

exposure rating for casualty per occurence XL - using severity distributions

Answer 5

use severity distribution based on industry statstics to estimate layer losses

GL & AL: distribution is used to obtain ILFs

WC: distibution is used to obtain ELFs

Question 6

ELFs can be approximated

Answer 6

using inverse power curve

aL^(-b)

Question 7

main difficulty in experience rating policies on umbrellas is

Answer 7

selecting appropriate severity trend

should add and subtract underlying limit as part of trending losses

trended umbrella = (umbrella loss+UL)*trend factor - UL

this trending procedure ignores new trended losses piercing umbrella policy

Question 8

ceding company is often willing to retain more losses in working layer and may use

Answer 8

use annual aggregate deductible as way to retain more loss and lower reinsurance premiums

• in that case, treaty becomes excess of aggregate treaty
• if deductibles are low enough, savings for annual aggregate deductible can be estimated using experience rating

Question 9

another loss sensitive feature

Answer 9

Swing plan which is type of retro rating

Question 10

aggregate distribution models, which we’ve previously used to price things like sliding scale commissions, involve using a range of LRs or loss costs instead of individual amounts

-can be done in several ways

Answer 10

1. empirical distribution
2. single distribution models
3. recursive calculations
4. other collective risk models

Question 11

empirical distribution

Answer 11

– use historical experience

-does not account for all possible outcomes and actual results may differ greatly from historical averages

Question 12

single distribution models

Answer 12

– assume aggregate losses follow known distribution

• advantage of being simple to use even when source data is limited
• no allowance for loss free scenario (lognormal) and no easy way to reflect impact of changing per occurrence limits on aggregate losses

Question 13

recursive calculations

Answer 13

– frequency is assumed to be Poisson, negative binomial, or binomial and severity is defined in discrete equally spaced amounts

• advantage of being simple to work with and providing accurate handling of low frequency scenarios
• inconvenient of higher expected frequencies due to # calculations and only single severity distribution can be used

Question 14

other collective risk models

Answer 14

– collective risk model is one in which frequency and severity are analyzed separately

recursive is example

-collective risk model is usually very good way to produce aggregate distributions but need to use some caution

Question 15

caution reasons

Answer 15

a. complexity of calculations can lead to black box mentality
b. assumption of frequency and severity being independent and each occurrence being independent of others may not be true
c. some models use numerical methods that have large error term for low frequency scenarios
d. aggregate distributions will reflect process variance of losses but not parameter variance of models used

Question 16

important feature of property CAT treaties

Answer 16

reinstatements

• these allow ceding company to refill treaty limit a certain number of times during policy period
• reinstatements can be pro rata as to amount of limit being refilled or pro rata as to time left on treaty or both
• reinstatements pro rata to time are not very popular due to seasonality of cats (pro-rata to time assume equal earnings through period)

Question 17

Pricing Property CAT covers

Answer 17

cat models are now standard approach for pricing property cat treaties

• historically, payback approach was used but now it is often just used as reasonability check on model results
• cat models are most recent method
• cat models require exposure info, coverage info for policies, geographical info, and details of any inuring reinsurance

Question 18

additional subjective considerations after a cat model is run:

Answer 18

a. WC exposure can be substantial for EQs if WC is covered in treaty
b. inuring reinsurance terms may not be calculable by model
c. fire following EQ exposure may exist even if EQs are not covered directly
d. coverage terms such as replacement cost vs actual cash value may significantly impact losses

Question 19

one important consideration in cat treaties is

Answer 19

basis of treaty since risks attaching treaties have potential for reinsurer to pay multiple times on same event

Question 20

finite risk covers

Answer 20

property cat covers with lower max losses compared to traditional treaties

Question 21

finite risk covers have 2 common characteristics

Answer 21

1. multiple year features
2. loss sensitive features (ie profit commissions)

Question 22

given low risk of finite covers , 2 conditions for ceding company to consider these reinsurance for accounting purposes

Answer 22

1. reinsurer assumes significant insurance risk
2. it is reasonably possible that reinsurer may realize a significant loss

Question 23

some complicating factors in pricing finite covers

Answer 23

Reinstatement provisions

Expenses

Carryforward provisions

Changes in premium and profit commissions by year of treaty

Cancellation provisions

Question 24

two advantages of using catastrophe models to help price property reinsurance compared to using the payback approach

Answer 24

• Catastrophe models incorporate actual exposure information, while the payback approach does this subjectively. • Catastrophe models incorporate actual risk location information, while the payback approach does this subjectively. • Catastrophe models can also be used to measure portfolio diversification, while the payback approach cannot do this. • Catastrophe models use the best scientific knowledge available about natural disasters to help estimate their impact. • Catastrophe models are much easier to scale from individual risks to the entire industry than the payback approach

Question 25

why carryforward provision is used

Answer 25

This is used to help stabilizere insurer results, and also to give insurers incentives to continue to control losses once their loss ratio passes the loss ratio corresponding to the minimum commission.

Question 26

Panjer’s recursive formula - works well for

Answer 26

low frequency scenarios, which is the case here due to the small number of claims. However, it does have the disadvantage in that only a single severity distribution can be used in the analysis