Mildenhall Chapter 6

Question 1

3 Ways Risk Measure Can Be Selected

Answer 1

1. Ad-hoc method: judgementally select a risk measure and then rationalize it based on the fact that it has desired properties or disagree with it if it has undesirable properties
2. Economic Method: select a risk measure based on economic theory. generally difficult to apply in practice
3. Characterization method: determine the desirable properties of a risk measure, then select a measure that satisfies these characteristics

Question 2

Desirable Properties of Risk Measure

Also for premium calculation principles (PCP) = pricing risk measures

Answer 2

DATE MT

• Monotone and Translation Invariance - intuitive and theoretically sound
• Diversification - should be reflected
• Allocation - can be allocated to segments
• Theoretical Soundness - consistent with a general theory
• Explainable - must be able to explain in order to “sell” it to users

Question 3

Further Desirable Properties

Answer 3

• Elicitability - can be estimated via regression-like techniques
• Robustness or Continuity - a small change in inputs should result in a small change in measured risk, the measured risk is continuous in the data
• Backtesting - measured risk is and can be sowne to be consistent with observations

Question 4

Desirable Characteristics of Risk Margins

Answer 4

1. Risk margin should be higher the lesser we know about the current estimate and its trend
2. Risk margin should be higher if they have low frequency high severity than vise versa
3. For similar risks, risk margin should be higher for contracts that persist over a longer time frame
4. Risk margin should be higher for risks with wider probability distribution
5. If emerging experience reduces uncertainty, risk margin should decrease. If increases uncertainty, then vise versa

Question 5

Why is VaR is not a suitable risk margin?

Answer 5

1. VaR is not subadditive, but may not be a major issue in practice
2. VaR ignores how severe the losses can be at the tail, but ignoring the tail does make the method more robust

Workaround: generate VaR at several different thresholds
Alternative: use TVaR - this is subadditive and tail sensitive

Question 6

Gradations of Tail-Thickness

Answer 6

Tail risk is the hardest to quantify (compared to volume and volatility)
1. No mean - thickest tail. impossible to insure, these distributions are killers, break the rules. Law of large number does not apply. Sum of iid may converge to a stable distribution with alpha <= 1
2. Mean, but no variance - still very thick tailed. LLN applies but central limit theorem does not. Sum of iid converse 1 < alpha < 2
3. Mean and variance, but finite moments - LLN and CLT does apply, higher moments such as skewness and kurtosis may not exist

Question 7

Risk Measure Intended Purpose

Answer 7

Intended Purpose: addressing the goal or question
* individual risk pricing
* classification ratemaking
* portfolio management
* determining risk capital or assessing held capital adequacy

Question 8

Risk Measure Intended Users

Answer 8

Intended User: any person that the actuary believes that will rely on the output
* Underwriter and/or pricing actuary: price adequately or allocate cost of capital
* Management or ERM: relative performance / portfolio optimization / reinsurance strategy
* Insured: value of insurance, assess solvency of insurer
* Regulator: minimum capital standards
* Rating agency: evaluating capital held
* Reinsurer: pricing assumed business
* Investor: compare risk and returns, access solvency of insurer

Question 9

Premium Calculation Principles (PCP)

AKA Pricing Risk Measures

Answer 9

do later

Question 10

Capital Risk Measures

Answer 10

do later