Brehm CH3 Flashcards
IRM (internal risk model) Startup: Staffing and Scope
- Organization chart (modeling team reporting line, solid line vs. dotted line reporting)
- Functions represented (Actuarial, finance, planning, underwriting, risk)
- Resource Commitment (mix of skill set, full time vs. part time)
- Critical roles and responsibilities (control of input parameters, control of output data, analyses and uses of output)
- Purpose (quantify variation around plan, or provide objective view of distribution of results)
- Scope (prospective UW year only, or including reserves, assets or operational risk?)
What does author recommend for staffing and scope for IRM?
- Reporting relationship (The reporting line for the IRM team is less important than ensuring they report to a leader who is fair)
- Resource commitment (Think of IRM implementation as the establishment of a new competency, which suggests transfer or outside hire of full-time employees)
- Inputs and outputs (controlled in a manner similar to that used for general ledger or reserving system)
- Initial scope (prospective underwriting period, variation around plan)
What parameter development details should be addressed for IRM?
- Modeling software (capabilities, learning curve, scalability)
- Developing input parameters (process is heavily data driven, requires expert opinion, many functional areas should be involved)
- Correlations (line of business representatives cannot set cross-line parameters, corporate-level ownership of these parameters required)
- Validation and Testing (no existing IRM with which to compare, multi-dimensional, multi-metric testing is required)
What does Author recommend for parameter development in IRM?
- Modeling software (comparing existing vendor software with user-bult options, ensure final software choice aligns with capabilities of the IRM team)
- Parameter Development (include product expertise from underwriting, claims, planning and actuarial. Develop a systematic way to capture expert risk opinion)
- Correlate (have the IRM team recommend correlation assumptions)
- Validation (validate and test over an extended period)
What implementation details should be addressed in IRM?
- Priority setting (importance of priority, approach and style (ask vs. mandate), priority and timeline must be driven from the top)
- Interest and impact (Communications plans, education plans)
- Pilot test (assign multidisciplinary team (actuarial, UW, finance, planning, risk), provide real data, real analysis on the business as a whole or on one specific segment. This is a learning and familiarization exercise)
- Education process (run in parallel with pilot test, bring leadership to same point of understanding)
What does author recommend for the implementation in IRM?
- Priority setting (have top management set the priority for implementation)
- Communications (plan for regular communication to broad audiences)
- Pilot test (allows effective preparation of the company for the magnitude of change)
- Education (target training to bring leadership to similar base level of understanding)
What integration and maintenance details should be addressed in IRM?
- Cycle (integrate into major corporate calendar (planning, reinsurance purchasing, capacity allocation), and ensure that IRM output supports major company decisions)
- Updating (determine frequency and magnitude of updates)
- Controls (centralize storage and control of input sets and output sets, endorsed set of analytical templates)
What does the author recommend for IRM integration and maintenance process?
- Cycle (integrate into planning calendar at a minimum)
- Updating ( perform a major input review no more frequently than semi-annually. minor updates can handled by modifying the scale of the impacted portfolio segments)
- Controls (maintain centralized control of inputs, outputs and possibly even application templates)
3 risks for modeling parameter uncertainty
- estimation risk
- Projection risk
- model risk
Describe estimation risk
arises from having only a sample of the universe of possible claims to use for estimating the parameters of distributions
Describe projection risk
the possible error in projecting past trends into future
Describe model risk
uncertainty that arises from having the wrong models to start with
Describe a simple trend model
- A trend line is often fit to loss cost history to project future levels of loss cost.
- Prediction intervals can be placed around this project to provide a quantification of projection risk
Assumption of the simple trend model
There is a single underlying trend rate which has been constant throughout the period of the historical dta and will remain constant in the future throughout the projection period.
Problem with simple trend model
The historical data is often based on estimates of past claims which have not yet settled. This increases the projection uncertainty. This can arise with projections of average claim cost (because of opens claims estimates), and claim frequency rates (due to IBNR).
Solution: more advanced regression procedures can correct the prediction intervals for the effect of uncertainty in the historical points.
Differences between severity trend and general inflation
- Severity trend has often been greater than general inflation. The excess trend is often described as social inflation or superimposed inflation.
- Claim severity trend is usually modeled from insurance data with no regard to general inflation.
Advantage of projecting superimposed inflation and general inflation separately
It reflects the dependency between claim severity trend and general inflation.
Describe First order autocorrelated time series (AR-1)
- This is the simplest form of a mean-reverting time series.
- The true underlying mean is unknown and estimated from the data (similar to simple trend model). However, it includes an autocorrelation coefficient and the annual disturbance distribution.
Why MLE (maximum likelihood estimation) is the preferred method for estimating parameters of frequency and severity distributions from historical data
- MLE has the smallest estimation error among unbiased estimators.
- MLE determines the parameters that maximize the probability of observing that data from a sample of that size from the distribution
For large data sets, the parameter distributions in the MLE procedure are multivariate normal. But why for smaller data sets, normality assumption creates problems?
- The standard deviation of the parameters can be high enough to give significant probability to negative values of the parameters.
- For heavy-tail distributions, the distribution of the parameters can itself be heavy-taield.
What’s a good distribution assumption for small samples
log-normal distributions
Approach to quantify estimation risk
use the standard covariance matric from MLE, but assume the parameters follow a joint lognormal distribution with that covariance matrix.
Procedures to select a model form
- Use the likelihood function and penalties for number of parameters. (use statistics like AIC, BIC, Hannan-Quinn Information Criterion (HQIC)
- Assign probabilities of being right to all the better-fitting distribution. Then use a simulation model to select a distribution from the better-fitting distributions. Then select the parameters from the joint log-normal distribution of parameters for that particular distribution.
Describe the characteristics of Frank Copula
- Frank copula produces weak correlation in the tails.
- C1 can be inverted.
- Typically won’t use it to model insurance losses
Describe the characteristics of Gumbel Copula
- More probability concentrated in the tails than Frank Copula
- It’s asymmetric, with more weight in the right tail
- Good candidate for insurance losses
- C1 is not invertible; ao it cannot be easily simulated (cannot solve for v)
Describe the characteristics of Heavy Right Tail (HRT) Copula
- Less correlation in the left tail and more in the right tail
- C1 is invertible so can solve for v (similar to Frank Copula)
- If X and Y are Burr distribution, then a joint Burr distribution is produced when the parameter of both Burrs is the same as that of the HRT
Describe characteristics of Normal Copula
- Right tail is lighter than Gumbel or HRT but heavier than the Frank Copula
- Left tail is similar to the Gumbel
Advantage of Normal Copula
- Easy simulation method
- Generalizes to multi-dimensions
