Brehm 3 CF Only Flashcards
a) Briefly describe four organizational details that need to be addressed when developing an internal model.
b) For each organizational detail, provide a recommended course of action.
Part a:
⇧ Reporting relationship – modeling team reporting line, solid line vs. dotted line reporting
⇧ Resource commitment – mix of skill set (actuarial, UW, communication, etc.), full time vs. part time
⇧ Inputs and outputs – control of input parameters, control of output data, analyses and uses of output
⇧ Initial scope – prospective UW year only, or including reserves, assets, operational risks? low detail (on the whole company) or high detail (on specific segment)?
Part b:
⇧ Reporting relationship – the reporting line for the internal model team is less important than ensuring they report to a leader who is fair
⇧ Resource commitment – since an internal model implementation is considered a new competency,
it’s best to transfer internal employees or hire external employees for full-time positions
⇧ Inputs and outputs – controlled in a manner similar to that used for general ledger or reserving systems
⇧ Scope – prospective UW period, variation around plan
a) Briefly describe four parameter development details that need to be addressed when developing an internal model.
b) For each parameter development detail, provide a recommended course of action.
Part a:
⇧ Modeling software – capabilities, scalability, learning curve, integration with other systems
⇧ Developing input parameters – process is heavily data driven, requires expert opinion (especially when data quality is low), many functional areas should be involved
⇧ Correlations – line of business representatives cannot set cross-line parameters, corporate level ownership of these parameters is required
⇧ Validation and testing – no existing internal model with which to compare, multi-metric testing is required
Part b:
⇧ Modeling software – compare existing vendor software with user-built options, ensure final software choice aligns with capabilities of the internal model team
⇧ Developing input parameters – include product expertise from UW, claims, planning and actuarial; develop a systematic way to capture expert opinion
⇧ Correlations – have the internal model team recommend correlation assumptions, which are
ultimately owned at the corporate level
⇧ Validation and testing – validate and test over an extended period, provide basic education to interested parties on probabilities and statistics
a) Briefly describe four model implementation details that need to be addressed when developing an internal model.
b) For each model implementation detail, provide a recommended course of action.
Part a:
⇧ Priority setting – importance of priority (company may not immediately make the necessary improvements to support implementation), approach and style (ask vs. mandate), priority and timeline must be driven from the top
⇧ Interest and impact – implement communication and education plans across the enterprise
⇧ Pilot test – assign multidisciplinary team (actuarial, UW, finance, etc.) to provide real data and real analysis on the company as a whole or on one specific segment, important to remember that piloting means model indications receive no weight (just a learning exercise)
⇧ Education process – run in parallel with pilot test, bring leadership to same point of understanding regarding probability and statistics
Part b:
⇧ Priority setting – have top management set the priority for implementation
⇧ Interest and impact – plan for regulator communication to broad audiences
⇧ Pilot test – assign multidisciplinary team to analyze real company data; prepare the company for the magnitude of change resulting from using an internal
⇧ Education process – target training to bring leadership to similar BASE level of understanding
a) Briefly describe three integration and maintenance details that need to be addressed when developing an internal model.
b) For each integration and maintenance detail, provide a recommended course of action.
Part a:
⇧ Cycle – integrate model runs into major corporate calendar (planning, reinsurance purchasing, capacity allocation), ensure that internal model output supports major company decisions
⇧ Updating – determine frequency and magnitude of updates
⇧ Controls – ensure that there is centralized storage and control of input sets and output sets (date stamping vital), ensure there is an endorsed set of analytical templates used to manipulate internal model outputs for various purposes (such as decision making and reporting)
Part b:
⇧ Cycle – integrate into planning calendar at a minimum
⇧ Updating – perform major input review no more frequently than twice a year. Minor updates can be handled by modifying the scale of the impacted portfolio segments
⇧ Controls – maintain centralized control of inputs, outputs and application templates
Briefly describe three ways in which parameter risk manifests itself.
⇧ Estimation risk – arises from using only a sample of the universe of the possible claims to estimate the parameters of distributions
⇧ Projection risk – arises from projecting past trends into the future
⇧ Model risk – arises from having the wrong models to begin with
A consultant has been asked to model projection risk for two independent firms. Based on the
number of annual claims, one firm is considered “small” and the other firm is considered “large.”
Given the following assumptions:
⇧ Projected losses are determined by multiplying aggregate losses by a factor 1 + J
⇧ Claims frequency is Poisson distributed for both firms
⇧ The severity CV for both firms is 5
a) Assuming that projection risk is zero (i.e. CV (1+J) = 0), compare the overall uncertainty for each firm.
b) For each firm, explain how the overall uncertainty changes as projection risk increases.
Part a:
⇧ When the frequency and severity distributions are known, the CV of total losses is calculated as the square root of “the frequency variance-to-mean ratio plus the square of the severity CV , all divided by the frequency mean.” Thus, the small firm should have more uncertainty since we are dividing by a smaller number (i.e. the number of claims)
Part b:
⇧ As the projection risk increases, the overall uncertainty for the large firm is more significantly impacted. This is because the small firm is already volatile to begin with
To project future losses, an actuary fit a trend line to historical data. Using standard statistical procedures, the actuary placed prediction intervals around the projected losses. Explain why these prediction intervals may be too narrow.
⇧ Historical data is often based on estimates of past claims which have not yet settled. In the projection period, the projection uncertainty is a combination of the uncertainty in each historical point AND the uncertainty in the fitted trend line. Thus, the actuary’s prediction
intervals may be too narrow due to the missing uncertainty associated with the historical data
a) Describe two approaches for modeling claim severity trend.
b) Explain why projecting superimposed inflation and general inflation separately is advantageous.
Part a:
⇧ Approach 1: Model severity trend from insurance data with no regard to general inflation
⇧ Approach 2: Correct payment data using general inflation indices. Then, model the residual superimposed inflation. Since any subsequent projection is a projection of superimposed inflation only, a separate projection of general inflation is required
Part b:
⇧ An advantage of projecting superimposed inflation and general inflation separately is that it reflects the dependency between claim severity trend and general inflation. Most enterprise risk models include a macroeconomic model, which includes future inflation rates. It is essential that the claim severity trend model reflects appropriate dependencies between claim severity trend and inflation. In doing so, inflation uncertainty is incorporated into projection risk
a) Describe the primary difference between modeling projection risk using a simple trend model and modeling projection risk using a time series.
b) Compare the prediction intervals constructed using a simple trend model with those constructed using a time series.
c) Briefly describe a consequence of parameterizing a time series with limited data.
Part a:
⇧ The simple trend model described earlier assumes that there is a single underlying trend rate that has been constant throughout the historical period and will remain constant in the future. A time series assumes that the future trend rate is a mean-reverting process with an autocorrelation coefficient and an annual disturbance distribution
Part b:
⇧ In the simple trend model, the prediction intervals widen with time due to the uncertainty in the estimated trend rate. In the time series model, the prediction intervals widen with time as well, but the effect is more pronounced and the prediction intervals are wider. This
is due to the additional uncertainty of the auto-regressive process
Part c:
⇧ If the time period of the data is too limited to exhibit a range of behaviors, the resulting model will be limited as well, and will understate the projection risk
a) Briefly describe how estimation risk is assessed using maximum likelihood estimation (MLE).
b) Briefly describe a situation in which estimating parameters using maximum likelihood estimation (MLE) is difficult.
c) For large datasets, the parameter distributions in the MLE procedure are multivariate normal. Briefly describe two problems that may arise when this normality assumption is used for a small dataset.
Part a:
⇧ To assess estimation risk, we use the covariance matrix that results from the standard MLE procedure (based on second partial derivatives of the parameters), but we assume the parameters follow a joint log-normal distribution with that covariance matrix (works for both large and small datasets)
Part b:
⇧ The best-fitting parameters can be difficult to determine if the likelihood “surface” is very flat near the maximum. When the surface is flat near the maximum, a wide range of parameter sets have almost the same likelihood. Thus, the set that maximizes the likelihood might not be any better than one that has slightly smaller likelihood
Part c:
⇧ The standard deviations of the parameters can be high enough to produce negative parameter values with significant probability
⇧ The distribution of the parameters may be heavy-tailed (the bi-variate normal is not heavytailed)
When building a model, various rules and metrics are used to select the best model form. However, the selected form may still be wrong. Describe a process to overcome this problem.
⇧ Assign probabilities of being right to all of the better-fitting distributions. These probabilities can be based on the Hannan-Quinn Information Criteria (HQIC) metric or a Bayesian analysis
⇧ Use a simulation model to select a distribution from the better-fitting distributions
⇧ Select the parameters from the joint log-normal distribution of parameters for the selected distribution
⇧ Simulate a loss scenario using the parameterized distribution
⇧ Start the process over again with the next scenario
