Clark

Question 1

Surplus Share

How to calculate? Given retained line and # of lines

Answer 1

Given retained line
Surplus Lines = # of lines * retained line
1. Risk #
2. Insured Value
3. Retained Portion = min[retained line, insured value]
4. Reinsured Portion = min[surplus lines, “above retained” (2) - (3)]
5. Surplus Percent = % ceded = (4) / (2)

Treat this like a XoL to calculate Ceded %:
* Loss = Insured Value
* AP = Retained Line | Limit = # of lines * Retained Line
* Ceded % = Reinsured Portion / Insured Value

Question 2

Profit Commission

What is it? Formula?

Answer 2

Returns some of reinsurer’s profit to the ceding company, incentivize ceding company to minimize losses

Reinsurer Profit = 1 - Treaty LR - Ceding Commission - Reinsurer Expense

Profit Commission = Reinsurer Profit * Percent Returned

Question 3

Loss Corridors

What is it? Example

Answer 3

Loss corridor allow for ceding company to reassume some liability if the loss ratio exceed a certain amount.

E.g. ceding company reassumes 75% of the losses between a 80% and 90% LR

Question 4

Loss Occuring vs. Risk Attaching
GNEPI vs. GNWPI

Answer 4

Loss occuring - losses occured during the treaty period
Risk attaching - losses attached to those policies written in the treaty period

Use EP for loss occurring
Use WP for risk attaching

Question 5

Ceding Commission

What is it? + Purpose

Answer 5

The ceding commission paid to the primary insurer is necessary as the primary insurer has much higher underwriting expenses when writing risks

Question 6

Annual Aggregate Deductible

What is it? How to calculate reinsurance portion?

Answer 6

Ceding company can use an AAD to retain more losses in the working layer and lower reinsurance premiums

1. Calculate losses that would of been ceded to reinsurer if NO AAD
2. Add those losses to the AAD and the coverage kicks in after

Another benefit - AAD can be estimated using experience rating

Excess charge factor phi = integral AAD to inf (y-AAD) g(y) dy / E(y)

g(y) = distribution of aggregate losses in the layer

Question 7

Swing Plans

What is it? How to calculate? Balanced? Cash Flow Advantage

Answer 7

Type of retrospective rating - can be applied to single or multiple treaty years

Retro Premium = Actual Layer Losses * Expense Load
Min/Max Premium = % * Subject Premium
Capped Retro Premium using ^

ELR for plan = E[Loss Cost] / E[Retro Premium]
Balanced plan if ELR = 1 - Expense Load

Provisional rate < E[Retro Premium] then cash flow advantage to primary insurer because he is paying less upfront and more later. Vise versa

Question 8

Exposure Factor

PPR Exposure, Casualty XOL Exposure, ALAE scenarios

Answer 8

Property Per Risk Exposure
* Exposure factor = P(AP + Limit / IV) - P(AP/IV)
* Linear interpolate if needed

Casualty XOL Exposure ALAE Pro-Rata
* Exposure Factor = [ ILF(AP + Limit) - ILF(AP) ] / ILF(Policy Limit)
* Exposure Factor = ( E[X; AP+Lim] - E[X;AP] ) / E[X;Policy Lim]
* Cap the AP + Limit and AP by the policy limit
* Use ALAE/Prem ratio, but also apply the exposure factor here

Casualty XOL Exposure ALAE w/ Loss
* Divide the AP + Lim and AP by (1 + % ALAE)

E[Treaty Loss] = SEP * ELR * Exposure Factor
Loss Cost = E[Treaty Loss] / SEP

Question 9

Exposure Factor > Worker’s Comp

Excess Loss Factors

Answer 9

ELF = ( E[X] - E[X;Limit] ) / E[X]
* E[X] using limited severities

Exposure Factor = ELF(AP) - ELF(AP+Limit)

E[Treaty Loss] = SEP * ELR * Exposure Factor
Loss Cost = E[Treaty Loss] / SEP

Question 10

Exposure Factor > Umbrella

Answer 10

Exposure Factor = [ ILF(AP+Lim+UL) - ILF(AP+UL) ] / [ ILF(Policy Limit+UL) - ILF(UL) ]
* Cap numerator to Policy Limit + UL