Bahnemann

Question 1

Claim Size Distributions

Answer 1

Pareto (Linear XS severity as limit increases)

Exponential (Constant XS severity at all limits)

Lognormal (XS Sev increases without bound)

Gamma (XS Sev decreases to asymptote)

Question 2

Claim Count Distributions

Answer 2

Poisson
Negative Binomial

Question 3

ILF Risk Load

Answer 3

Reflects added volatility on top of higher expected value

Question 4

Straight Deductible

Answer 4

All losses above d are reduced by d

Question 5

Franchise Deductible

Answer 5

All losses above d are paid in full

Question 6

Diminishing Deductible

Answer 6

Losses between d and D have linearly decreasing deductible

All losses above D are paid in full

Question 7

XS Policy - Applying Lower and Upper Limit

Answer 7

Lower first, then upper limit

(a,a+l]

width l

Question 8

Ded Policy - Applying Lower and Upper Limit

Answer 8

Upper limit first, then lower

(a,l]

width l-a

Question 9

Impact on CV as impose additional limits

Answer 9

Decreases

Question 10

CV of XS claims vs Ground-Up

Answer 10

XS has larger CV than ground-up

Question 11

Different Tau’s (Trend)

Answer 11

Tau_X - ground-up claim size inflation

~Tau_X - XS claim size inflation

~Tau_N - Claim count inflation due solely to claim size inflation

Tau_Freq - Frequency Trend

~Tau_S - Agg XS loss inflation due to claim size inflation

~Tau_S,Total = Tau_Freq * ~Tau_N * ~Tau_X

Question 12

Tau Key Relationships

Answer 12

1. If ground-up claim size inflation positive then Agg XS inflation larger
2. If negative, Agg Xs inflation more negative

This is because of claim count inflation due to claim size inflation

Question 13

Contagion Parameter

Answer 13

Reflects the fact that occurence of a claim often leads to additional claims

Question 14

What does premium cover

Answer 14

Expected Loss
General Expenses (Incl. ULAE)
UW Profit
Risk Charge

Question 15

Risk Charge

Answer 15

Covers contingencies

Process Risk and Parameter Risk

Increased uncertainty at higher limits

Question 16

2 Criteria for Exposure Unit

Answer 16

1. Meaningful indicator of policy’s expected number of claims
2. Determine expected number of claims associated with a singe exposure unit

Question 17

2 Methods for ILFs

Answer 17

1. Empirical
2. Parametric (better for higher limits where data sparse)

Question 18

3 ALAE Methods

Answer 18

1. Included in Loss
2. % of Loss (Multiplicative)
3. Avg Amount (Additive)

Question 19

ILF Consistency Test

Answer 19

Looking at layers of constant width, premium for succesive layers decreases as attachment point increases

Increases at decreasing rate