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exam 7 > Verrall > Flashcards

Verrall Flashcards

1
Q

what is one aspect that has been missing from the literature on stochastic reserving?

(Verrall)

A

the idea of adjusting the results based on actuarial judgment or other expert knowledge

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2
Q

what are two examples of situations where results may need to be adjusted?

(Verrall)

A
  • change in payment pattern due to a change in company policy
  • legislature has enacted benefit limitations that restrict the potential for loss development
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3
Q

what is the problem with adjusting model results based on expert opinion?

(Verrall)

A

it disrupts the assumptions underlying the stochastic model

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4
Q

what are two areas where expert knowledge is applied?

Verrall

A
  • BF method

- insertion of prior knowledge about individual dev. factors in the CL method

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5
Q

what are two important properties of Bayesian models?

Verrall

A
  • can incorporate expert knowledge

- can be easily implemented

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6
Q

how do Markov chain Monte Carlo (MCMC) methods simulate the posterior distribution?

(Verrall)

A

by breaking the process down into a number of simulations that are easy to carry out

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7
Q

what is a common problem with Bayesian methods?

Verrall

A

-can be difficult to derive the posterior distribution, which may be multidimensional

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8
Q

how do MCMC methods make the simulation easier to work with?

Verrall

A

they use the conditional distribution of each parameter, given all the others

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9
Q

what is the difference between the BF method and the CL method?

(Verrall)

A
  • BF method uses an external estimate for the ‘level’ of each row
  • CL uses the data in each row
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10
Q

what is an advantage of Mack’s model?

Verrall

A

parameter estimates and prediction errors can be obtained using a spreadsheet (simple!)

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11
Q

what are two disadvantages of the Mack model?

Verrall

A
  • no predictive distribution

- additional parameters must be estimated in order to calculate the variance

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12
Q

what is the general form of the ODP model?

Verrall

A
  • model for incremental losses

- uses a GLM approach with a log link function

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13
Q

what does the term “over-dispersed” (in ODP) mean?

Verrall

A

-variance is PROPORTIONAL to the mean, NOT EQUAL to the mean

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14
Q

what are two disadvantages of the ODP model?

Verrall

A
  • requires column and row sums of incremental values to be positive
  • hard to see the connection to the CL method in the formulation
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15
Q

what type of claims can the over-dispersed negative binomial model be applied to?

(Verrall)

A

both incremental and cumulative claims

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16
Q

what is an advantage of the over-dispersed negative binomial model?

(Verrall)

A

-mean is exactly the same as the CL method, reserve estimates are too

17
Q

how does the normal approximation to the negative binomial model adjust the ODNB model?

(Verrall)

A

replaces the negative binomial with a normal distribution whose mean is unchanged, but whose variance is altered to allow for negative incremental claims

18
Q

what is a disadvantage of the normal approximation to the negative binomial model?

(Verrall)

A

additional parameters must be estimated in order to calculate the variance

19
Q

how can the mean squared error of prediction (MSEP) be obtained?

(Verrall)

A

prediction variance = process variance + estimation variance

20
Q

what is the square root of the MSEP?

Verrall

A

the root mean squared error of prediction, aka prediction error

21
Q

what is the difference between standard error and prediction error?

(Verrall)

A
  • standard error is the square root of the estimation variance
  • prediction error considers both the uncertainty in parameter estimation and the inherent variability in the data being forecast
22
Q

what are two advantages of Bayesian methods?

Verrall

A
  • full predictive distribution can be found using simulation methods
  • RMSEP can be obtained directly by calculating the standard deviation of the distribution
23
Q

what are two cases of an actuary intervening in the estimation of the development factors for the CL method?

A
  • dev factor is changed in some rows due to external information
  • dev factors are based on a five-year volume-weighted average rather than all of the available data in the triangle
24
Q

what does the variance W depend on? [in the case where a factor is changed in some rows due to external info]

(Verrall)

A
  • W depends on the strength of the opinion
  • large W pulls dev. factor closer to CL dev. factor
  • small W pulls dev. factor closer to the prior mean
25
Q

when using a Bayesian model for the BF method, for a given choice of M_i, how can the variance be altered?

(Verrall)

A

changing the value of beta_i

26
Q

what does a larger value of beta_i imply when using a Bayesian model for the BF method?

(Verrall)

A

implies we are more sure about the value of M_i

27
Q

what does it mean to choose prior distributions with large (small) variances when using a Bayesian model for the BF method?

(Verrall)

A
  • small beta -> large variance -> low confidence (no prior knowledge) in our parameter estimates -> result close to CL method
  • large beta -> small variance -> high confidence (prior knowledge) in our parameter estimates -> result close to BF method
28
Q

what are two options to estimate the column parameters (y_j) whe using a Bayesian model for the BF method?

(Verrall)

A
  • use plug-in estimates from the traditional CL method with no variability
  • define prior distributions for the column params, and estimate them FIRST (before prior distr. for row params and estimating those) -> PREFERRED
29
Q

why is it preferred to define prior distributions and estimate the column parameters?

(Verrall)

A

-allows us to take into account that the column params have been estimated when calculating the prediction errors, predictive distribution, etc. -> fully stochastic version of the BF method

30
Q

how should we think of prediction error, when comparing prediction errors?

(Verrall)

A

-as a percentage of the prediction, since the reserve estimate itself may vary greatly from model to model

31
Q

how do prediction errors change with confidence in prior distributions?

(Verrall)

A

-prediction errors should increase as less confidence is placed in prior distributions

exam 7 (21 decks)

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