Miccolis - Theory of ILs and XOL pricing

Question 1

Provide two reasons why insurers may be subject to adverse selection by insureds that purchase high liability limits.

Answer 1

1. Policy limits might influence claims settlements. Juries may be more likely to award higher damages when an insurance policy will cover this amt.
2. Insureds with higher loss potential purchase higher limits

Question 2

Define process risk and parameter risk

Answer 2

Process risk: variation b/t actual losses and expected losses can be the result of stochastic or random nature of the freq and severity of insurance losses.

Parameter risk: variation result from an inability to estimate expected loss accurately.
e.g. error in estimation of inflation trends, sampling error in loss experience

Question 3

Discuss one reason that a set of ILFs may fail consistency test yet still generate reasonable prices

Answer 3

Anti-selection - where insureds that are more likely to have large losses buy higher limits, or jury verdicts where the verdict is based on limit

Question 4

Three general properties of expected value ILFs.

Answer 4

1. ILF strictly increase
2. ILFs increase at a decreasing rate
3. ILF’’ can never be positive

Question 5

How to demonstrate if anti-selection is affecting ILFs

Answer 5

compare ILFs with population ILFs

Question 6

Explain how the consistency tests had both a mathematical interpretation and a practical meaning

Answer 6

Mathematically: that ILF curve is increasing at a decreasing rate

Practically: does not make sense to pay more for each additional 1000 coverage when the prob. of loss > limit is smaller than that for a lower limit.

Question 7

How can severity distribution assumption impact the effect inflation has on avg increase in excess loss

Answer 7

Heavier tail, then more loss would be in excess layer, lightening the impact of excess inflation.

Question 8

List two reasons for favorable selection

Answer 8

1. Financially secure insured with more to protect may be better risks
2. Insurance companies, knowing these insureds are better risks, offer them higher limits.

Question 9

List 3 problems with developing a severity distribution from experience data + 2 from Rosenburg’s

Answer 9

1. immature losses from recent policy year
2. distribution bias, result from data on losses generated from different limits
3. credibility at high end is a concern
4. cluster pts: maybe artificial
   [] appear at points other than policy limits
   [] case reserves are often rounded
5. Gaps, intervals with no claims