Multiple Testing in Loss Reserving Liu Leping, Gao Lei Bootstrapping ODP Model ODP model Bootstrapping ODP model A practical problem Multiple runs test, FDR control and block bootstrap Runs test BH’s FDR Control Algorithm Block bootstrapping A real example . . . . . . Multiple Testing in Loss Reserving: False Discoveries in Estimated Reserving Risk Liu Leping Gao Lei Department of Statistics Tianjin University Of Finance and Economics 2014 年 6 月 27 日
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MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
Multiple Testing in Loss Reserving: False Discoveries inEstimated Reserving Risk
Liu Leping Gao Lei
Department of StatisticsTianjin University Of Finance and Economics
2014 年 6 月 27 日
MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
Stochastic claims reserving
This has become a newacademic dicipline
Numerous papers appeare inacademic journals
A book has appeared
There is a Wikipedia page
Google scholar search for ”Stochastic claims reserving”
Mario V. Wüthrich Wüthrich & Merz(2008)
MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
Bootstrapping: the last 20 years(England,2010)
The holy grail of stochastic reservingtechniques is to obtain a predictivedistribution of outstanding liabilities.
One method that has been proposedto produce a simulated predictivedistribution is Bootstrapping.
MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
Content
1 Bootstrapping ODP Model
2 Multiple runs test, FDR control and block bootstrap
3 A real example
MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
Content
1 Bootstrapping ODP ModelODP modelBootstrapping ODP modelA practical problem
MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
The over-dispersed Poisson model
ODP model assumption(Renshaw & Verall,1998)
Xi,j,incremental payments.Xi,j ∼ ODP(mi,j, ϕj)
E[Xi,j] = mi,j = xi ∗ yjVar[Xi,j] = ϕj ∗ mi,j
log(mi,j) = c + αi + βj.
R function:glm()
MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
Bootstrapping ODP model
Step of bootstrapping ODP model(England & Verall, 1999, 2002, 2006).1 Fit the model and obtain fitted values m̂ij
2 Calculate the residualsri,j =
Xij − m̂i,j√ϕjm̂ij
.
3 Resample residual r∗ij4 Obtain pseudo data
X∗ij = r∗ij
√ϕjm̂ij + m̂ij.
5 Refit ODP model to estimate the future incremental payments6 Simulate forecast incremental payments from process distribution7 Repeate many times and store the simulated forecast payment
MultipleTesting in
Loss Reserving
Liu Leping,Gao Lei
BootstrappingODP Model
ODP model
BootstrappingODP model
A practicalproblem
Multiple runstest, FDRcontrol andblockbootstrap
Runs test
BH’s FDRControl Algorithm
Blockbootstrapping
A real example
. . . . . .
A practical problem:violation of independence assumption
1 Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical andpowerful approach to multiple testing[J]. Journal of the Royal StatisticalSociety. Series B (Methodological), 1995: 289-300.
2 England P, Verrall R. Analytic and bootstrap estimates of prediction errors inclaims reserving[J]. Insurance: mathematics and economics, 1999, 25(3):281-293.
3 England P D, Verrall R J. Stochastic claims reserving in general insurance[J].British Actuarial Journal, 2002, 8(03): 443-518.
4 England P D, Verrall R J. Predictive distributions of outstanding liabilities ingeneral insurance[J]. Annals of Actuarial Science, 2006, 1(02): 221-270.
5 Wüthrich M V, Merz M. Stochastic claims reserving methods in insurance[M].John Wiley & Sons, 2008.
6 Joseph Lo A. Extending the Mack Bootstrap: Hypothesis Testing andResampling Techniques[J]. The Actuarial Profession, 2011.
7 Verrall R J, Wüthrich M V. Reversible jump Markov chain Monte Carlomethod for parameter reduction in claims reserving[J]. North AmericanActuarial Journal, 2012, 16(2): 240-259.