Brehm #3

Question 1

Parameter risk

Answer 1

risk of assuming incorrect distributions or parameters for those distributions

Question 2

Components of parameter risk (3)

Answer 2

1. estimation risk
2. projection risk
3. model risk

Question 3

Estimation risk

Answer 3

uncertainty arising from having only a sample of possible data to estimate parameters

Question 4

Largest source of parameter risk

Answer 4

projection risk

Question 5

Coefficient of variation of total claims and what it measures

Answer 5

CV ( S ) = [ ( Var ( N ) / E [ N ] + CV ( X )^2 ) / E [ N ] ] ^ .5

*measure of projection risk
larger CV = more risk

Question 6

Relationship b/w size and risk for CV

Answer 6

more risk for smaller companies

however, as projection risk increases, rises more for large companies because small companies are already volatile

Question 7

Components of projection uncertainty (2)

Answer 7

1. uncertainty associated with historical data

2. uncertainty in fitted trend line

Question 8

Relationship b/w claim severity trend and general inflation

Answer 8

claim severity trend > general inflation

> > excess is called social inflation or superimposed inflation

Question 9

Relationship b/w uncertainty and time when analyzing trend

Answer 9

prediction intervals widen over time (b/c of uncertainty in the trend rate)

Question 10

Method to assess estimation risk

Answer 10

use the covariance matrix from MLE procedure and assume the parameters come from a joint lognormal distribution

Question 11

What is a copula?

Answer 11

combination of individual marginal distributions into a multivariate distribution to force correlation in specific areas

F ( x, y ) = Pr ( X < x and Y < y ) = C ( u, v )
or = C ( F ( x ), F ( y ) )

where u, v are percentiles of X and Y

Question 12

Simulation process using copulas (3 steps)

Answer 12

1. random draws, u and p, where p is a draw from the conditional distribution so p = C-sub 1 ( u, v )
2. invert C-sub 1 by solving for v
3. invert marginal X and Y distributions by setting F ( x ) = u and F ( y ) = v and solving for x and y

Question 13

Which copulas (3) are invertable and why does this matter?

Answer 13

1. Frank
2. Normal
3. HRT

** if copulas are invertable, they can be simulated

Question 14

Common copula ranks in terms of right tail correlation (least to most)

Answer 14

Frank < Normal < Gumbel < HRT

Question 15

Purpose of tail concentration functions / L-R graph

Answer 15

provides a quantification of tail strength

> > L ( z ) and R ( z ) are measures of correlation

Question 16

L-R graph

Answer 16

L ( z ) and R ( z ) against z which exists on [0,1]

Question 17

Left tail function - L ( z ) and lower tail dependence parameter

Answer 17

L ( z ) = C ( z, z ) / z

lower tail dependence parameter = limit of L ( z ) as z&raquo_space; 0

Question 18

Right tail function - R ( z ) and upper tail dependence parameter

Answer 18

R ( z ) = ( 1 - 2 * z + C ( z, z ) ) / ( 1 - z )

upper tail dependence parameter = limit of R ( z ) as z&raquo_space; 1

Question 19

Methods to model projection risk (2)

Answer 19

1. Simple fixed trend model
2. Auto correlated time series

Simple trend model understates projection risk especially for long tailed lines

Question 20

Methods to compare tail behavior between 2 copulas (2)

Answer 20

1. Left-right tail dependence (L-R graphs)

2. Plot joint density functions and compare density in the tails

Question 21

Components of an internal risk model (IRM - 4)

Answer 21

1. Startup
2. Parameter development
3. Implementation
4. Integration and maintenance

Question 22

Recommendations for IRM startup (4)

Answer 22

1. Reporting relationship - fair and balanced leader more important than functional reporting line
2. Resource commitment - establishing a new competency - best to transfer or hire full time employees
3. Control of inputs and outputs
4. Initial scope - prospective UW period and variation around plan

Question 23

Recommendations for parameter development in an IRM (4)

Answer 23

1. Modeling software - capabilities, scalability, and integration with other systems as well as user capabilities
2. Parameter development - involves many functional areas (UW, claims, planning, and actuarial), heavily data driven but requires expert opinion - ensure clear ownership of final parameters
3. Correlations - cannot set cross lines parameters in isolation, should have corporate level ownership
4. Validation - test over an extended time period

Question 24

Recommendations for implementation of an IRM (4)

Answer 24

1. Priority setting - should come from sr management (more efficient)
2. Communication - plan for regular communications to a broad audience
3. Pilot testing - prepare company for magnitude of change
4. Education - bring leadership to a base level of understanding

Question 25

Recommendations for integration and maintenance for an IRM (3)

Answer 25

1. Cycle - integrate into corporate calendar, especially into planning process
2. Updating - major reviews not more than semi-annually
3. Controls - maintain centralized control of inputs, outputs, and possibly application templates