Clark

Question 1

Describe the 2 main methods by which reinsurance can be applied

Answer 1

1. Facultative reinsurance
   Reinsurance designed and purchased separately for each individual risk of ceding company
2. Treaty reinsurance
   Single reinsurance contract allows reinsurer to cover multiple risks of ceding company

Question 2

Describe the 2 main types of Treaty Reinsurance

Answer 2

1. Proportional
   Reinsurer assumes same % of losses an premium
2. Non-proportional
   Reinsurer assumes losses in XS of retention limits.
   Also known as XOL reinsurance.

Question 3

Describe the 2 main types of Proportional Treaty Reinsurance

Answer 3

1. Quota Share
   % is same across all risks
   Reinsurer will also pay ceding comm to ceding company to reflect larger UW expenses incurred
2. Surplus Share
   % varies by risk
   When ceding company wants to retain low risk policies & only cede high risk policies

Question 4

Explain how losses are split between retained and ceded for Surplus Share reinsurance

Answer 4

Tot surplus lines = Retained line * # of lines purchased

If risk below retained line, keeps in full

If insured value above retained line, reinsurer assumes % of loss, ALAE & premium of:
max(0%, min(SurplusLines, InsValue - RetainedLine)/InsValue)

Question 5

Describe the 3 types of Non-proportional reinsurance treaties

Answer 5

1. Per Risk XL
   Reinsurer assumes losses between retention and limit for each risk
   Protects ceding company against large individual claims
2. Per Occurrence XL
   Reinsurer assumes losses between retention and limit for each occurrence across multiple risks.
   Commonly used as CAT reinsurance
3. Aggregate XL
   Reinsurer assumes losses between retention and limit for aggregate tot losses for a given time period (usually 1y)
   Offers frequency protection primarily.

Question 6

Briefly explain the pricing paradox

Answer 6

If you can precisely price a given contract, ceding company will not want to buy it.

If historical is stable enough to provide data to make a precise expected losses estimate, then reinsured will be willing to retain that risk.

Question 7

Describe the difference between risk attaching and losses occurring bases.

Answer 7

Risk attaching:
All policies beginning or renewing during reinsurance contract are covered regardless of when losses occur or are reported.
Losses on PY basis
WP

Losses occurring:
All claims occurring during reinsurance contract period are covered regardless of policy inception or when losses are reported.
Losses on AY basis
EP

Question 8

Describe the 2 main methods for pricing reinsurance

Answer 8

1. Experience rating
   Use adjusted historical experience of either reinsurance contract or ceding company to calculate E(Loss) of prospective reinsurance contract.
   Primary approach used to price proportional reinsurance.
2. Exposure rating
   Use current risk profile and estimated loss distribution to calculate E(Loss) of prospective reinsurance contract.
   Often used in combination with experience rating to price non-proportional reinsurance.

Question 9

List adjustments made in experience rating of reinsurance contract

Answer 9

1. On-level premium
2. Trend exposures and premiums
3. Develop losses at ultimate
4. Trend losses
5. Replace cat losses with cat loading
6. Load expenses

Question 10

Define subject premium

Answer 10

Non-proportional treaties have rate expressed as % of ceding company’s premium potentially subject to treaty.

Question 11

Define burn cost

Answer 11

Rate based solely on experience rating (aka experience rate)

Question 12

Define burning cost

Answer 12

Unadjusted ratio of past ceded losses to past subject premium.

Question 13

List and advantage and a disadvantage of experience rating for reinsurance contract

Answer 13

+: use ceding company’s actual experience

-: experience is volatile and maybe outdated

Question 14

List an advantage and a disadvantage of exposure rating for reinsurance contract

Answer 14

+: uses ceding company current mix of business

-: Loss distribution used may not be good fit for risks being priced

Question 15

Describe the steps to price proportional treaty using experience rating

Answer 15

1. Compile historical experience on treaty (5 or more years)
2. Exclude CAT and LL
3. Develop and trend losses, on-level and trend premiums and exposures.
4. Select expected non-cat loss ratio for treaty
5. Load for CATs
6. Estimate other expenses & CR
7. Decide whether CR is acceptable or not

Question 16

If CR is not acceptable, list 3 adjustments reinsurer can suggest

Answer 16

1. Lowering ceding commission
2. Introducing occurrence limits
3. Introducing adjustable features: sliding scale commissions, loss corridors, etc.

Question 17

Describe Sliding Scale Commissions

Answer 17

When commission paid by reinsurer to ceding company varies with actual loss ratio on treaty, subject to max and min commission.

Provisional commission is paid at start of treaty and adjusted up or down later based on actual loss experience of treaty and scale.

E(Comm_range) = Comm_high + slide*(LR_high - AvgLR)

Question 18

Define Expected Technical Ratio

Answer 18

ETR = ELR + Expected Comm Ratio

Question 19

Briefly explain how sliding scale commissions can create CF advantage

Answer 19

Any difference between provisional commission and expected commission would give a CF advantage to either reinsurer or ceding company.

Expected > Provision = Adv to reinsurer

Expected < Provision = Adv to insurer

Question 20

Briefly describe Carryforward Provision

Answer 20

Sliding Scale Commissions may also have carryforward provision, which means actual LR > LR corresponding with min commission.

Carryforward provision = LR prior - LR mincomm

Provision is added to LR in next year for determination of next year’s commissions.

Question 21

Why do we use carry forward provision

Answer 21

In the long run, this helps smooth results.

Question 22

Describe the 2 approaches to estimate impact of carry forward provisions.

Answer 22

1. Decrease LR in each bracket of sliding scale by carry forward amount.
2. Model sliding scale based on long-run expected impact of contract.
   Expands method 1 to span of several years instead of just 1.
   Serves to reduce aggregate variance by factor of # of years in block.

Question 23

Identify a disadvantage of method 1 to estimate impact of carry forward provision

Answer 23

This assumes any past carry forward amounts only apply to current year’s LR.

Question 24

Identify a disadvantage of method 2 to estimate impact of carry forward provision

Answer 24

Ignores fact that contract may non-renew, giving reinsured no carry forward benefit.

If comm deficit can be carried forward, but credits cannot, potential for non-renewal is exacerbated.

Question 25

Briefly describe the impact of positive carry forward provision on next year's commission (all else being equal)

Answer 25

If carry forward > 0, E(Comm) for next year will decrease, all else being equal.

Question 26

Calculate Profit Commission

Answer 26

Profit commissions return some of reinsurer's profit to ceding company as additional commissions. Also based on actual LR and increases commission with low result. Reins Profit = 1 - Actual Treaty LR - Ceding Comm - Reins Expense Margin % Profit Comm = Reins Profit * % returned $ Profit Comm = Actual Ceded P * % Profit Comm

Question 27

Calculate LR Net of Loss Corridors

Answer 27

Loss corridors allow ceding company to reassume some liability if LR > certain amount. Avg LR Net of corridor = min(AvgLR, Layer_min + max(AvgLR, Layer_max) - Layer_min, 0)*(1-corr) + max(AvgLR - Layer_max,0))

Question 28

Describe the impact of Loss Corridor on reinsurer ELR

Answer 28

Loss Corridor decreases reinsurer ELR.

Question 29

Calculate experience rating loss cost for Prop per risk XL treaty

Answer 29

1. Gather historical data (ideally 10y since larger losses) 2. On-level subject premiums and trend premium & exposures 3. Trend losses & determine amount in reinsurance layer 4. Apply LDFs to developped layer losses 5. Calculate LR for each historical year and take average 6. Load expenses

Question 30

Describe the 2 ways ALAE can be handled

Answer 30

1. Included with loss Sum up trended loss & trended ALAE and treat it as a single amount when comparing to limit and retention Covered = max(0, min(limit, Loss+ALAE - retention)) 2. Pro-rate with loss Calculate portion of trended loss covered by treaty Assume same % of trended ALAE will also be covered Loss covered = max(0, min(limit, loss - retention)) ALAE covered = (loss covered/loss) * ALAE

Question 31

Calculate exposure rating loss cost for Prop per risk XL treaty

Answer 31

Done using exposure curves P(p): expected loss capped at % p of IV divided by expected unlimited loss. P(p) = E(X;pIV) / E(X) = 1 - XS ratio (p) Exposure factor = P(ret+lim / IV) - P(ret / IV)

Question 32

State an advantage of exposure rating

Answer 32

Current risk profile is modelled not what was written years earlier + very helpful when data is sparse.

Question 33

Can we use the same exposure curves for different risk sizes.

Answer 33

Ideally not. Ow assume scale independence: prob of $10K loss on $100K risk = prob of $100K loss on $1M risk) Scale independence is not realistic in practice, particularly for commercial insurance.

Question 34

Discuss 3 issues on Property per Risk Treaties

Answer 34

1. Free cover Arises when there is no loss experience in highest portion of layer. Experience away would give away any XS coverage for which there is no loss experience. 2. Credibility for experience rating Lack of credibility will reduce appropriateness of experience-rated indicated loss costs. 3. Inuring reinsurance When XS treaty applies on top of another, need to adjust. Need to restate historical to be net of of inuring reinsurance.

Question 35

Explain how to deal with Free Cover

Answer 35

Use experience rating for lower portion of layer and then use exposure rating relativities applied to lower layer experience loss cost to price higher portion of layer.

Question 36

Describe 3 layers of Casualty per Occurrence XL Treaties

Answer 36

1. Working layer Lower layer expected to be hit, often multiple times per year. A perfect working layer would produce stable enough results to be retained by ceding company. 2. Exposed Excess Layer Sees losses less frequently and sometimes not at all during a given year. Experience rating may still be used to price this layer. 3. Clash Cover layer Usually only hit due to multiple policies involving a single occurrence (ex: cats) Could also be hit by Extra Contractual Obligations (ECO) or rulings awarding damages in XS of policy limits. Could be hit by single policy depending on how ALAE is included.

Question 37

Describe the steps for experience rating a Casualty per occurrence XL Treaty

Answer 37

1. Gather historical data 2. On-level and trend premium and exposures 3. Apply severity trend to losses and ALAE 4. Sum trended losses by year and apply excess LDFs 5. Divide trended and developped layer losses by adjusted subject premium to get loss costs by year.

Question 38

Explain 2 methods to deal with policy limits in Casualty per occ XL treaties

Answer 38

1. Apply historical policy limit to each trended loss Ignores fact that limits tend to increase over time 2. Apply trend factor to historical loss without policy limit cap (& adjust subject premium to reflect premium that would have applied at higher limit) Assumed limits increase with inflation

Question 39

Which data should be used to derive excess LDFs

Answer 39

Ideally, ceding company data Otherwise, industry data published by RAA, but caution: 1. Report lag can vary by company and may include several layers of lag 2. Mix of retention and limits is not clearly broken out (can distort LDFs) 3. Data may contain asbestos and environment claims (may distort patterns)

Question 40

Use exposure rate to price Casualty per occ XL treaty

Answer 40

As with property exposure rating, we can use distribution related to claim severity based on industry statistics to estimate layer losses. For WC, distribution is used to obtain ELFs = E(X) - E(X;L) / E(X) Once exposure curve (sev distribution) is known, you can obtain exposure factor: (ILF(AP+Lim) - ILF(AP)) / ILF(PL) AP = Attachment Point Then apply exposure factor to expected losses (net of inuring reinsurance).

Question 41

How is the exposure rating formula different if ALAE pro-rata

Answer 41

Exposure factor = E(X;min((AP+Lim)/(1+e),PL) - E(X;min(PL,AP/(1+e)) / E(X;PL) e is % ALAE applied to trended loss limited to PL

Question 42

Discuss 2 issues with loading ALAE in casualty per occ XL treaties and how can we resolve

Answer 42

1. Both methods assume ALAE varies directly with capped indemnity. Not good assumption since you can have ALAE and no indemnity + large claims do not tend to have proportional ALAE This tends to result in overestimating ALAE in higher layers 2. In formula with e, it can result in exposure factor of 0 applying to higher layer that could actually be hit since ALAE can exceed selected loading. These issues can be resolved by modeling ALAE to loss relationship: ELFs can be approx by aL^(-b) a and b can be estimated from selected XS ratios found in NCCI retro manual.

Question 43

In Casualty per occ XL treaties, which 3 distributions can be used to obtain E(X;L)

Answer 43

1. Truncated Pareto E(X;L) = pS + ((1-p)/(Q-1))*((B+QT)-(B+L)*(B+T)*Q/(B+L)) T is truncation point p is prob of small loss S is avg small severity 2. Log-Logistic (special case of Truncated Pareto with B=0 and Q=1) E(X;L) = pS + (1-p)T(1-ln(T/L)) 3. Mixed Exponential E(X;L) = sum of wj*uj*(1 - exp(-L/uj))

Question 44

Identify 2 disadvantages of using Truncated Pareto in Casualty per occ XL treaties

Answer 44

1. Only apply to losses > T 2. Excess factors for higher layers become very dependent on Q

Question 45

Briefly explain how umbrella policies are a problem for casualty excess treaties

Answer 45

Umbrella policies differ from standard excess insurance since they usually provide broader coverage not tied to underlying policy definitions. If written above primary policies from ceding company, can be treated as single policy with higher limit. If ceding company does not write underlying policy, it becomes more difficult to price treaty.

Question 46

Define umbrella insurance

Answer 46

Liability coverage in excess of other policies where coverage is limited or non-existent.

Question 47

Calculate exposure factor for umbrella policy without drop-down coverage

Answer 47

Trended Umbrella Loss = (Loss + Underlying Limit)*TrendFactor - Underlying Limit Ignores new trended losses piercing umbrella policy. Exposure Factor = (E(X;min(UL+PL,UL+AP+Lim))-E(X;min(UL+PL,UL+AP))) / (E(X;UL+PL)-E(X;UL))

Question 48

Define drop-down coverage

Answer 48

If underlying policy agg limits exhausted, umbrella will drop-down to provide primary coverage.

Question 49

Calculate exposure factor for umbrella policy drop-down coverage.

Answer 49

Exposure Factor = (E(X;UL+min(PL, AP+Lim))-E(X;UL+min(PL, AP))(1-phi)+(E(X;min(PL,AP+Lim))-E(X;min(PL,AP))*phi) / ((E(X;UL+PL)-E(X;UL))*(1-phi)+phi*E(X;PL)) phi is the agg excess charge (analogous to table M charge)

Question 50

Describe 2 loss-sensitive features

Answer 50

1. Annual Aggregate Deductibles (AAD) Enables ceding company to retain losses in working layer, subject to specified limit. XS treaty then covers aggregate losses in layer. Excess charge = integral of (y-AAD)*g(y)/E(y) 2. Swing Plans Type of retro rating, can be applied to single treaty or block of treaty years combined. Retro P = (Actual Layer Loses)*100/ELR ELR is before accounting for max/min

Question 51

Briefly explain why swing plans are not balanced and how to correct for this (3)

Answer 51

Because load is 100/ELR. To correct for this, you can: 1. Change expense load 2. Change max rate G 3. Change min rate H

Question 52

Briefly explain how discount is an issue for WC treaty experience rating

Answer 52

Tabular discounts may distort experience rating. To unravel discount, individual claim costs need to be projected into treaty layer. This require demographic info and cost info.

Question 53

List 4 ways to construct aggregate distribution models

Answer 53

1. Empirical distribution 2. Single distribution 3. Recursive calculations 4. Other Collective Risk Models

Question 54

Explain the empirical distribution method to construct aggregate distribution models. Give 1 advantage and 2 disadvantages.

Answer 54

Use historical experience +: Easy to calculate -: Does not account for all possible outcomes (not reliable if limited data) -: Volatility may be understated if volume or mix has changed significantly over time or if smoothing development technique is used (ex: B-F)

Question 55

Explain the single distribution method to construct aggregate distribution models. Given 1 advantage and 2 disadvantages.

Answer 55

Assume agg losses follow known distribution, such as lognormal. Distribution can be fit to historical data and then prob and expected losses within each range of agg losses can be calculated using distribution formulas. +: Easy to use even with limited source data -: No allowance for loss-free scenario (undefined at l=0) -: No easy way to reflect impact of changing per-occ limits.

Question 56

Explain the recursive calculations method to construct aggregate distribution models. Give 1 advantage and 2 disadvantages.

Answer 56

Panjer's recursive algorithm formula generates agg loss distribution given equally-spaced discrete severity distribution with spacing h and claim counts N distribution that satisfies f(n) = (na+b)*f(n-1)/n +: Easy to work with -: Calculation is painful for higher frequency -: Can only use 1 severity distribution

Question 57

Explain the Other Collective Risk Models method to construct aggregate distribution models. Give 1 advantage and 2 disadvantages.

Answer 57

Explicitly recognize frequency and severity Recursive calculation is an example of collective risk model +: Very good way to produce aggregate distribution -: Complexity of calculation can lead to black box mentality -: Assume independence of occurrences and freq/sev -: Can produce large error terms in low-free scenarios -: agg distribution shows process variance but not parameter variance

Question 58

For lognormal, calculate sigma^2, u, E(Y:L)

Answer 58

sigma^2 = s^2 = ln(CV^2 + 1) u = ln(mean) - (s^2)/2 E(Y;L) = exp(u+s^2/2)*Phi((lnL-u-s^2)/s) + L*(1 - Phi((lnL-u)/s)

Question 59

Which distribution satisfy the Panjer's recursive formula requirement

Answer 59

1. Poisson a = 0 b = u f(0) = exp(-u) 2. NB a = 1-p b = (a-1)(1-p) p is prob of failure f(0) = p^a 3. Binomial a = p/(p-1) b = (M+1)p/(1-p) p if prob of success M is # trials f(0) = (1-p)^M

Question 60

Explain how to use the Panjer's recursive algorithm

Answer 60

A0 = p0 A1 = p1f1 pk = (a+b/k)pk-1 so A1 = (a+b)p0*f1 = (a+b)f1A0 A2 = p1f2 + p2f1^2 = (a+b)f2A0 + (a+b/2)f1A1 A3 = (a+b)f3A0 + (a+2b/3)f2A1 + (a+b/3)f1A2 ... Ak = sum of Ak-1*fi*(a+b/k)*i if Poisson: Ak = sum of u*i*fi*Ak-i*(1/k) Mean = u*(xf1+2xf2+3xf3+...) Var = u*(fi*x^2+f2*(2x)^2+f3*(3x)^3+...)

Question 61

Calculate E(S) and V(S)

Answer 61

E(S) = E(N)E(X) V(S) = E(N)V(X) + V(N)E^2(X)

Question 62

Calculate reinstatement premiums for CAT treaties.

Answer 62

Reinstatements allow ceding company to "refill" treaty limit a certain # of times during policy period. Assume any reinstatements will be automatically applied after any loss covered by treaty: Agg limit = (1+#reinst)*occ limit Pro-rate to amount: Reinst P = Annual P * Reinst provision * Actual Covered Losses/Occ Limit Pro-rata to amount and time: Reinst P pro-rate to amount * (months left / 12)

Question 63

Briefly explain why pro-rata to amount and time is not very popular for cats treaty.

Answer 63

Due to seasonality of CATs, uniform distribution of loss exposure assumptions is violated

Question 64

Explain the payback approach to price cat treaties.

Answer 64

CAT models are now standard approach for pricing property cat treaties, but historically, payback approach was used. Now often used as reasonability check on model results. Payback period = Treaty Limit / Annual Premium Rate on Line = Annual Premium / Treaty Limit

Question 65

State 4 subjective considerations in pricing CAT treaty after model is run

Answer 65

1. WC exposures can be substantial for eqk if WC is covered in treaty 2. Inuring reinsurance terms may not be calculable by model 3. Fire following eqk exposure may exist even if eqk are not covered directly. 4. Coverage terms such as replacement cost vs actual cash value may significantly impact losses.

Question 66

Discuss how risk attaching treaties have potential to pay multiple times for same event

Answer 66

An additional complication is the need to write contracts correctly such that reinsurer is not potentially twice liable for one loss. This happens in risk attaching treaties if effective dates of underlying policy do not line up with effective dates of reinsurance treaty. Underlying policy is covered by 2 different treaties since treaty renews in middle of policy term. To avoid overpayment, many treaties include an interlocking clause to apportion losses that may be covered under more than one contract.

Question 67

Define finite risk covers

Answer 67

Finite risk covers are property cat covers with lower max losses compared to traditional treaties. They have 2 common characteristics: 1. Multiple year features 3y contract may allow for cancellation after 1 or 2 years if premiums exceed losses. 2. Loss-sensitive features Profit comm, additional premium, etc.

Question 68

State the 2 conditions for ceding company to consider finite risk covers as reinsurance for accounting purposes

Answer 68

1. Reinsurer assumes significant insurance risk 2. It is reasonably possible that reinsurer realize significant loss

Question 69

List 4 complicating factors in pricing finite risk cover treaties

Answer 69

1. Reinstatement provisions 2. Expenses 3. Carryforward provisions 4. Changes in premium 5. Profit comm by year 6. Cancellation provisions

Question 70

Calculate Final Price of Treaty

Answer 70

Prem = (Loss Cost*(1+ULAE%) + f)/(1-v)

Question 71

Reinsurance premium need to cover reinsurer's expected losses + which 3 other things?

Answer 71

1. Timing of CFs (impact investment income which contributes to profitability) 2. Risk load for risk exposure to reinsurer 3. Profit provision for reinsurer

Question 72

Briefly describe 4 types of information required by catastrophe model

Answer 72

1. Measure of exposure Insured values, construction types, occupancies, attachment points for XS contracts. 2. Geographical information Property address info is converted into latitude and longitude coordinates by geocoding engine. Insured value info may be less precisely aggregated by zip code or state, resulting in less precise model results. 3. Terms of the insurance policies Deductible and coinsurance provisions of original policies. 4. Details of inuring reinsurance If SS inures to benefit, any features such as occurrence caps or loss corridors will affect CAT exposure.