Marshall

Question 1

Risk Margin For Normal and Lognormal Distribution

Answer 1

Normal
* Z * CoV
* norminv(%-tile,0,CoV)

Lognormal
* Var = σ^2 = ln(1 + CoV^2)
* Risk margin = exp(-Var/2 + Z * SD) - 1

Question 2

Independent Risk

What are they?

Answer 2

Parameter risk - randomness associated with the insurance process, makes it difficult to select appropriate parameters

Process risk - pure randomness associated with the insurance process

Question 3

Internal Systemic Risk

Specification Error

What is it + good indicators

Answer 3

Impossible to build a model that is fully representative of the insurance process
* Many different models used
* Model separately analyses different claim/payment types (ideally homogenous groups modeled separately)
* Little variation in range of results produced by model
* Checks made on reasonability of results (business leader acceptance, expert peer review, reconcilate changes in liabilities, diagnostic checks on outcomes, benchmark against industry data)
* Subjective adjustments to factors (fewer the better)
* Detects trends in claim cost
* Detailed analysis and quantify superimposed inflation (legislative changes, things that increase claim cost but not real inflation)
* Detailed expense analysis
* Ability to model using more granular data, like claim level data

Question 4

Internal Systemic Risk

Parameter Selection Error

What is it + good indicators

Answer 4

It’s impossible to pick all the right parameters (but we can get close)
* Best predictors (may or may not be used in model) with strong correlation to claim cost have been identified and analyzed
* Best predictors are stable over time or change due to process changes (not b/c they’re unstable)
* Modeled value of predictors used rather than subjectively selected, and lead claim cost outcome rather than lag (inflation predictor up –> claim cost up rather than claim cost up –> inflation predictor up)

Question 5

Internal Systemic Risk

Data Error

What is it + good indicators

Answer 5

Poor data, unavailable data, and/or inadequate knowledge of the data
* Credible knowledge of past processes and changes in processes that affects predictors
* Consistent and reliable information from business (proactive 2-way communication with claims staff, underwriters, etc)
* Data is reocnciled against other sources and against prior analysis with differences explained
* Robust and replicable process for obtaining data (no or low potential for miscoding, etc)
* Ideally no prior instants of data revisions. But if there is, understand how frequent and how severe
* Ideally no known/current data issues. But if there is, understand possible impacts on predictions

Question 6

External Systemic Risk

Examples

Answer 6

• Economic and social risks (inflation, unemployment, interest rates, etc)
• Superimposed inflation (legislative changes, courrt rulings)
• Changes in claims reporting/payment patterns, case reserve estimation process, etc
• Expense risk from policy maintenance and claim handling
• Event risk - a single event which triggers a large number of claims (ex. catastrophe)
• Recovery risk - reinsurance, S&S recoveries

Question 7

Correlation Effects

Independent, Internal systemic, External systemic

Answer 7

Independent Risk
* Assumed to be uncorrelated with any other source of uncertainty/risk

Internal Systemic Risk
* Uncorrelated with the other 2
* May have some correlation between classes and/or liabilities (same actuary estimating liabilities across classes, likely a linkage between premium liability and reserve methods)

External Systemic Risk
* Uncorrelated with the other 2
* May have some correlation between classes and/or liabilities