Mildenhall Chapter 2 + 3 Flashcards
(9 cards)
Risk: Uncertainty of achieving objectives
Pure/Insurance, Speculative/Asset, Financial Risk
Pure/Insurance risk - possible bad outcome with no potential of good outcome (e.g. loss on an insurance policy)
Speculative/Asset Risk - could have good or ad outcome (e.g. insurance, premium - loss/expense, is a speculative risk)
Financial Risk - uncertainty of financial outcomes - uncertainty in timing, amount or both (e.g. insurance reduces financial risk of the insured by covering a portion of the loss and specifiying payment dates)
Systematic Risk vs Systemic Risk
Defintion and example
Systematic Risk - cannot be reduced by diversification
(e.g. cats, will impact many insureds)
Systemic Risk - where an individual event can cause a chain reaction of additional events (cats are not systemic, does not trigger additional cats)
Labeling Risky Outcomes
Explicit Representation
What is it? Pro/Con
Identifies an event by providing specific details about it (sample space is interpretable sample points e.g. EQ magnitude, epicenter)
E.g 9-digit catastrophe identifier
Pros - distinguishes between different events/outcomes, enables outcomes to be linked across a book of business risk, helps modeling dependence risk
Cons - if there’s too many possible events, or if events only impact a small portion of your book … unrealistic to tie an event to each individual policyholder
Labeling Risky Outcomes
Implicit Representation
What is it? Pro/Con
Identifies an outcome with its value (sample space is -∞ to ∞)
e.g. for losses, size of the loss
Pros - good if we only care about loss outcome rather than the cause of loss
Cons
* difficult to aggregate, no way to link different outcomes of an event.
* difficult to specify dependence
* cannot distinguish between different events with same outcome
Labeling Risky Outcomes
Dual Implicit Representation, Exceedance/Nonexceedance Probability
What is it? Pro/Con
Identifies the rank of the outcomes (sample space is 0 to 1)
e.g. investors assess bonds based on p(default) or catastrophe models summarized by exceedance prob
Useful when we don’t care about the amount of loss
Exceedance s = S(x) = P(X > x)
Non-Exceedance p = F(x) = P(X ≤ x)
Pros - easy to make comparisons, F(X) always lies [0,1]
Cons - difficult to aggregate
Risk Measures
Risk Preference Properties
- Complete - for any pair of losses X & Y, can conclude X ≽ Y, Y ≽ X, or both
- Transitive if X ≽ Y and Y ≽ Z then X ≽ Z
- Monotonic if X ≤ Y for all outcomes then X ≽ Y
Risk Measures
Risk Measure
What is it? What impacts it?
Risk measure (p) quantifies risk preference (via a number)
X ≽ Y <–> p(X) ≤ p(Y)
Factors
* Volume - smaller risks are preferred
* Volatility - lower volatility (variance / SD) is preferred
* Tail - lower likelihood of extreme outcomes is preferred
Risk Measures
Capital Risk Measure
What is it? Use cases?
Determines the assets needed to back an existing or hypothetical portfolio at a given level of confidence
Use cases
* management determining how much assets to set aside
* regulator determining minimum capital requirement
* rating agency to rate how adequate an insurer’s capital is (measure VaR or TVaR)
Risk Measures
Pricing Risk Measure
Determine the expected profit insureds need to pay in total to make it worthwhile for investors to bear the portfolio’s risk
The margin (prem - expected loss) needs to be high enough to attract necessar capital form investors
More sensitive to volatility