Cameron Mutual Insurance Company Data

Description

An illustrative dataset—a matrix (of the dimensions 10x10) with ten completed years of claims payment developments of the Cameron Mutual Insurance company from the period 1988 – 1997. The data matrix contains ten origin/occurrence years (in rows where the first row represents the incident year 1988) with ten consecutive development periods/years (in columns).

Usage

data(CameronMutual)

Format

CameronMutual

A simple 10x10 matrix of a class triangle with ten origin years (rows) each being fully developed within ten consecutive development periods/years (columns)

origin

matrix rows with the occurrence year (origin)

dev

matrix columns with the development period (development)

Details

The run-off triangle (the upper-left triangular part of the data matrix) contains only positive increments making the triangle suitable for the typical benchmark reserving approach—the over-dispersed Poisson model (GLM regression model).

In practice, the upper-left triangle (the run-off triangle) is typically observed (known) while the bottom-right triangular part of the data matrix is treated as a future payments outcome (an "unknown" truth) that should be estimated/predicted. The Cameron Mutual Insurance data matrix is fully observed (i.e., obtained retrospectively) to allow for some goodness-of-fit evaluations.

Source

https://www.casact.org/publications-research/research/research-resources
(PP Auto Data Set, NAIC group code: 5320)

References

Meyers, G. G. and P. Shi (2011). Loss reserving data pulled from NAIC Schedule P. Available from https://www.casact.org/publications-research/research/research-resources

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4 (Portfolio #1)

Guarantee Fund of the Czech Insurers' Bureau Data

Description

Illustrative datasets provided by the Guarantee Fund of the Czech Insurers' Bureau (GFCIB) for the mandatory car insurance in the Czech Republic. The quarterly based payments are aggregated in four run-off triangles with the paid amounts for four separate lines of business: bodily injury, material damage, technical provision, and annuities.

Usage

data(GFCIB)

Format

GFCIB

Four run-off triangles (objects of the class triangle) with the dimensions 60x60 with 15 origin years (provided on a quarterly basis in individual rows) and 60 development periods/quarters (columns)

origin

matrix rows with the occurrence quartal (origin)

dev

matrix columns with the development period (development)

Details

The data are structured in the the list object GCCIB with four elements—one for each line of business: \$bodilyInjury, \$materialDamage, \$provisions, and \$annuity. The run-off triangles are all aggregated over the period from the first quartal of 2008 (Q1) till the last quartal of 2022 (Q4).

Source

The Czech Insurers’ Bureau https://www.ckp.cz

Midwest Family Mutual Insurance Company Data

Description

An illustrative dataset—a matrix (of the dimensions 10x10) with ten completed years of claims payment developments of the Midwest Family Mutual Insurance company from the period 1988 – 1997. The data matrix contains ten origin/occurrence years (with the first row representing the incident year 1988) and ten consecutive development periods/years (in columns).

Usage

data(MidwestMutual)

Format

MidwestMutual

A simple 10x10 matrix of a class triangle with ten origin years (rows) each being fully developed within ten consecutive development periods/years (columns)

origin

matrix rows with the occurrence year (origin)

dev

matrix columns with the development period (development)

Details

The run-off triangle (the upper-left triangular part of the data matrix) contains only positive increments making the triangle suitable for the standard modelling approach—the over-dispersed Poisson model (GLM approach).

In practice, the run-off triangle only (the upper triangular part) of the data matrix is known while the bottom-right triangular part is treated as a future outcome (an "unknown" truth) that should be estimated/predicted. The Midwest Family Mutual Insurance data matrix is fully observed to allow for some retrospective goodness-of-fit evaluations.

Source

https://www.casact.org/publications-research/research/research-resources
(Other Liability Data Set, NAIC group code: 23574)

References

Meyers, G. G. and P. Shi (2011). Loss reserving data pulled from NAIC Schedule P. Available from https://www.casact.org/publications-research/research/research-resources

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4 (Portfolio #2)

Nevada General Insurance Company Data

Description

An illustrative dataset—a matrix (of the dimensions 10x10) with ten completed years of claims payment developments of the Nevada General Insurance company from the period 1988 – 1997. However, the data matrix only contains four non-zero origin/occurrence years (from the period 1994 – 1997) all being fully developed for ten consecutive development periods/years (in columns). The remaining matrix rows are all zeros. The resulting run-off triangle (the upper-left triangular part of the data matrix) is, therefore, sparse and very uninformative.

Usage

data(NevadaGeneral)

Format

NevadaGeneral

A simple 10x10 matrix of a class triangle with ten origin years (rows) each being fully developed within ten consecutive development periods (columns). However, only for development profiles are nonzero and standard (parametric) reserving techniques (e.g. the ODP model) are not applicable

origin

matrix rows with the occurrence year (origin)

dev

matrix columns with the development period (development)

Details

In practice, the reserve for such sparse run-off triangles is not estimated by any stochastic model but, instead, an expert judgement is used to set the reserve. Nevertheless, the nonparametric reserving provided by PARALLAX, REACT, or MACRAME can still achieve resonable reserve predictions

Source

https://www.casact.org/publications-research/research/research-resources
(PP Auto Data Set, NAIC group code: 10007)

References

Meyers, G. G. and P. Shi (2011). Loss reserving data pulled from NAIC Schedule P. Available from https://www.casact.org/publications-research/research/research-resources

S3 Method Class profileLadder

Description

A function to make the work with the functional development profiles within run-off triangles more easy and straightforward—particularly when vizualizing the functional profiles (observed, completed, or both simultaneously) in a single plot

Usage

as.profileLadder(x)

Arguments

Value

an object of the class profileLadder which is a list with the following elements:

See Also

parallelReserve(), mcReserve(), permuteReserve(), plot.profileLadder()

Examples

data(CameronMutual)
print(CameronMutual) 

x <- as.profileLadder(CameronMutual)

print(x)
plot(x)

First Occurrences of Covid-19 Cases in the Czech Republic

Description

An illustrative dataset—a matrix (of the dimensions 4x8) with the cumulative counts of the first reported cases of the Covid-19 pandemic in the Czech Republic. Four cohorts are defined by the Czech counties where the first reported case occurred during the period March 1st – 7th, 2020 (e.g., Prague, Vsetín, or Dečín), March 8th – March 14th (e.g, Brno, České Budějovice, Kladno, Mladá Boleslav, Plzeň), March 15th – March 21st (e.g., Chomutov, Český Krumlov, Písek, Tábor), and, finally, during the week in March 22nd – March 28th, 2020 (e.g., Jindřichův Hradec, Klatovy, Teplice).

Usage

data(covid19CZ)

Format

covid19CZ

A simple 4x8 matrix of a class triangle with four cohorts (rows) consecutively observed for 8 weeks (starting in March 1st 2020 with the first case in the first cohort (first row) reported in March 1st)

Details

The cumulative reported cases are provided in the table for 8 consecutive development periods (where each period represents seven consecutive days) starting in March 1st, 2020.

Source

Institute of Health Information and Statistics of the Czech Republic https://www.uzis.cz:443/

Exploration of Run-Off Triangle Increments

Description

The function takes a cumulative or incremental run-off triangle (partially or completely observed) and provides some basic exploratory of the observed incremental payments. The function serves as a useful tool for a user-based insight when manually defining the states of the Markov Chain that is used to drive the reserve prediction in the MACRAME algorithm implemented within the function mcReserve().

Usage

incrExplor(
  triangle,
  method = c("median", "mean", "max", "min"),
  out = 1,
  states = NULL,
  breaks = NULL
)

Arguments

Value

An object of the class mcSetup with the following elements:

References

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4

See Also

mcBreaks(), mcStates(), mcReserve(), permuteReserve()

Examples

data(CameronMutual) 

## default Markov Chain states with (roughly) equally occupied bins 
incrExplor(CameronMutual)

## five Markov Chain states (with roughly equally occupied bins)
incrExplor(CameronMutual, states = 5)

## explicitly defined breaks for five increment bins while the Markov states
## are obtained as medians of the increments within each bin
incrExplor(CameronMutual, breaks = c(20, 500, 1000, 2000))

## explicitly defined breaks for five bins and the Markov states
## are given as the maximum increments within each bin
incrExplor(CameronMutual, breaks = c(20, 500, 1000, 2000), method = "max")

## manually defined breaks for the bins and the corresponding states 
## exactly one state must be within each break
incrExplor(CameronMutual, breaks = c(20, 500, 1000), 
                          states = c(10, 250, 800, 1500))

Access Markov Chain Breaks for Run-Off Triangle Increments

Description

Retrieves the Markov chain components from the output of the incrExplor() function or the mcReserve() function. In particular, the function returns the set of breaks used to define the bins for the incremental run-off triangle increments.

Usage

mcBreaks(object)

Arguments

Value

The vector of the break points that define the set of bins for the run-off triangle increments.

See Also

mcReserve(), incrExplor(), mcStates(), mcTrans()

Examples

## DEFAULT performance of the incrExplor() function and the MACRAME algorithm
output1 <- incrExplor(CameronMutual)
output2 <- mcReserve(CameronMutual)

## Extracting the DEFAULT break points from both outputs
mcBreaks(output1)
mcBreaks(output2)

## Extracting the corresponding break points for 4 Markov states
mcBreaks(incrExplor(CameronMutual, states = 4))

MACRAME Based Development Profile Reserve

Description

The function takes a cumulative (or incremental) run-off triangle (partially or completely observed) and returns the reserve prediction obtained by the MACRAME algorithm (see Maciak, Mizera, and Pešta (2022) for further details).

Usage

mcReserve(
  chainLadder,
  cum = TRUE,
  residuals = FALSE,
  states = NULL,
  breaks = NULL
)

Arguments

Value

An object of the type list with with the following elements:

References

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4

See Also

incrExplor(), permuteReserve(), mcBreaks(), mcStates(), mcTrans()

Examples

## run-off (upper-left) triangle with NA values
data(MW2014, package = "ChainLadder")
print(MW2014) 

## MACRAME reserve prediction with the DEFAULT Markov chain setting 
mcReserve(MW2014, residuals = TRUE)

## complete run-off triangle with 'unknown' truth (lower-bottom run-off triangle)  
## with incremental residuals (true increments minus predicted ones)  
data(CameronMutual)
mcReserve(CameronMutual, residuals = TRUE)

## the same output in terms of the reserve prediction but back-fitted residuals 
## are provided instead (as the run-off triangle only is provided)
data(observed(CameronMutual))
mcReserve(observed(CameronMutual), residuals = TRUE)

## MACRAME reserve prediction with the underlying Markov chain with five 
## explicit Markov chain states
mcReserve(CameronMutual, residuals = TRUE, states = c(200, 600, 1000))

Access Markov Chain States in the MACRAME Algorithm

Description

Retrieves the Markov chain components from a profileLadder object returned from the function mcReserve() or the mcSetup object returned from the function incrExplor(). In particular, the function returns the vector of the states used by the underlying Markov Chain utilized for reserve prediction in the MACRAME algorithm.

Usage

mcStates(object)

Arguments

Value

The vector of the Markov chain states that are used by the MACRAME algorithm.

See Also

mcReserve(), incrExplor(), mcBreaks(), mcTrans()

Examples

## MACRAME reserve prediction with the DEFAULT Markov chain setup 
output <- mcReserve(CameronMutual)

## Extracting the corresponding Markov states
mcStates(output)

#' ## Extracting the corresponding states when explicit breaks are used
mcStates(mcReserve(CameronMutual, breaks = c(1000, 2000, 3000)))

Access Markov Chain Transition Matrix in the MACRAME Algorithm

Description

Retrieves the Markov chain components from a profileLadder object returned from the function mcReserve() – in particular, the function returns the matrix of the estimated transition probabilities used by the underlying Markov Chain to provide the reserve prediction.

Usage

mcTrans(object)

Arguments

Value

The matrix of the estimated Markov chain transition probabilities

See Also

mcReserve(), mcBreaks(), mcStates()

Examples

## MACRAME reserve prediction with the DEFAULT Markov chain setup 
output <- mcReserve(CameronMutual)

## Extracting the corresponding break points
mcTrans(output)

Observed Run-Off Triangle Layout vs. Predicted (Unknown) Layout

Description

Simple layout function to allow work with fully developed run-off triangles (i.e., completed squares that also contain typically unknown (future) claim payments). Such data are not common in actuarial practice but they are usefull for retrospective analysis and back-testing purposes.

Usage

observed(object, cum = TRUE)

Arguments

Value

If object is an integer value then the function returns a TRUE/FALSE layout matrix with the TRUE values for the observed (known) part of the run-off triangle (the upper-left triangular part of the matrix) and values FALSE otherwise. If object is a matrix (an object of the class matrix or triangle) then the function returns the observed (known) part of the run-off triangle with NA values elsewhere. Depending on the choice of the cum parameter, either a cumulative (DEFAULT) or incremental (cum = FALSE) run-off triangle is returned

See Also

plot.profileLadder(), parallelReserve(), mcReserve()

Examples

## observed/unobserved layout for the run-off triangle with 5 origins
print(observed(5))
print(!observed(5))

## fully observed run-off triangle with typically unknown (future) payments
## included in the lower-right triangular part for evaluation purposes
data(CameronMutual) ## the full data matrix
observed(CameronMutual) ## cummulative run-off triangle
observed(CameronMutual, cum = FALSE) ## incremental run-off triangle

Parallel Based Development Profile Reserve

Description

The function takes a cumulative (or incremental) run-off triangle (partially or completely observed) and returns the reserve prediction obtained by the PARALLAX or REACT algorithm (see Maciak, Mizera, and Pešta (2022) for more details). If a full data matrix is provided as the input then the algorithms uses only on the relevant part of the data—the run-off triangle only (i.e., the top-left triangular part of the matrix) but standard incremental residuals (true incremental payments minus predicted increments) are returned for retrospective validation purposes (if residuals = TRUE). If the run-off triangle is provided only,then the algorithm caclulates so-called back-fitted (incremental) residuals instead (see Maciak, Mizera, and Pešta (2022) for details).

Usage

parallelReserve(
  chainLadder,
  method = "parallax",
  cum = TRUE,
  residuals = FALSE
)

Arguments

Value

An object of the class profileLadder which is a list with the following elements:

References

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4

See Also

mcReserve(), permuteReserve(), summary.profileLadder()

Examples

## run-off (upper-left) triangle with NA values (bottom-right part)
data(MW2014, package = "ChainLadder")
print(MW2014) 
parallelReserve(MW2014, residuals = TRUE)

## completed run-off triangle with 'unknown' truth (lower-bottom part)  
## for the estimation purposes only the upper-left triangle is used 
data(CameronMutual)
parallelReserve(CameronMutual, residuals = TRUE)

## the previous output is identical (in term of the reserve prediction) 
## but back-fitted residuals are provided in the output instead 
print(observed(CameronMutual))
parallelReserve(observed(CameronMutual), residuals = TRUE)

Permutation Bootstrap Reserve (PARALLAX, REACT, MACRAME)

Description

The function takes a completed run-off triangle provided either by some classical parametric reserving technique (ODP model, Mack model, or Tweedie model) or some functional-based alternative (PARALLAX, REACT, or MACRAME) and estimates the overall reserve distribution in terms of the permutation bootstrap approach proposed in Maciak, Mizera, and Pešta (2022).

Usage

permuteReserve(object, B = 500, std = TRUE, quantile = 0.995, adjustMC = TRUE)

Arguments

Value

An object of the class permutedReserve which is a list with the following elements:

References

Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4

European Parliament and Council (2009). Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II). Official Journal of the European Union, 1–155.
https://data.europa.eu/eli/dir/2009/138/oj

See Also

parallelReserve(), mcReserve(), plot.permutedReserve(), summary.permutedReserve()

Examples

## REACT algorithm and the permutation bootstrap reserve 
data(CameronMutual)
output <- parallelReserve(CameronMutual, method = "react")
summary(permuteReserve(output, B = 100))

## MACRAME algorithm with a pre-specified number of states using the same MC 
## states and the same break for each permuted run-off triangle
output <- mcReserve(CameronMutual, states = 5)
plot(permuteReserve(output, B = 100, adjustMC = FALSE))

## Permutation bootstrap applied to a completed run-off triangle 
## obtained by a parametric Over-dispersed Poisson model (from ChainLadder pkg)
library("ChainLadder")
output <- permuteReserve(glmReserve(MW2008), B = 100)
summary(output, triangle.summary = TRUE)

Visualization of the Run-Off Triangle Increments for the Markov Chain

Description

The function provides a graphical visualization of the results obtained from the incrExplor() function. In particular, the considered run-off triangle increments are distributed into the bins according the given Markov chain breaks and states. Two figures are provided: The first figure contains a histogram of the standard incremental residuals with a conrresponding kernel density estimate. The second figure shows how the increments are distributed into the given set of bins (defined by the break points). In addition, the corresponding Markov chain states are displayed

Usage

## S3 method for class 'mcSetup'
plot(x, ...)

Arguments

Value

The function returns a layout with two plots: A histogram with the run-off triangle increments and the barplot with the increments being distributed into the given set of bins

See Also

incrExplor(), mcReserve()

Examples

## run-off triangle increments within the default bins
x <- incrExplor(CameronMutual)
plot(x)

## run-off triangle increments and user-defined number of bins
x <- incrExplor(CameronMutual, states = 5)
plot(x)

## run-off triangle increments within the user-specified bins
x <- incrExplor(CameronMutual, breaks = c(500, 1000, 1500))
plot(x)

Plotting the Output of the Permutation Bootstrap

Description

The function provides a graphical visualization of the results obtained from the permutation bootstrap (see Maciak, Mizera, and Pesta (2022) for further details) applied to the output of some parametric or nonparametric reserving technique. In particular, the classical parametric methods include GLM based reserving, the Mack Chain Ladder model, and the Tweedie model (all implemented in the package ChainLadder). Nonparametric (so-called functional-based) methods include three algorithms implemented in the ProfileLadder package (PARALLAX, REACT, and MACRAME)

Usage

## S3 method for class 'permutedReserve'
plot(x, ...)

Arguments

Value

The function returns a layout for four plots. The first panel shows a simple barplot type visualization of the estimated reserve, the estimated ultimate, and the true reserve (if available). The second panel provides a histogram for (permuted) bootstrapped reserves with a nonparametric estimate of the corresponding density. The third panel provides a detailed inspection of the bootstrapped ultimates (with true ultimates if provided) and, finaly, the last panel shows the observed diagonal vs. simulated ones.

See Also

permuteReserve()

Examples

## reserve estimated by MACRAME and the corresponding visualization
x <- mcReserve(CameronMutual)
plot(permuteReserve(x, B = 100))

Plotting Development Profiles

Description

The function provides a graphical representation of the functional profiles estimated by the PARALLAX, REACT, or MACRAME algorithm (see Maciak, Mizera, and Pesta (2022) for further details). The function takes an object of the class profileLadder which is the output of the parallelReserve() function or the mcReserve() function. Alternatively, the function can be also applied to visualise the run-off triangle itself—if the triangle is of the class profileLadder.

Usage

## S3 method for class 'profileLadder'
plot(
  x,
  xlab = "Development period",
  ylab = "Cumulative claims",
  main = "",
  default.legend = TRUE,
  ...
)

Arguments

Value

A graph with the observed functional development profiles from the input run-off triangle, the estimated/predicted functional segments (i.e., functional profile completion provided by the corresponding estimation method—PARALLAX, REACT, or MACRAME) the and the true future profiles (if these are available)

See Also

as.profileLadder(), parallelReserve(), mcReserve()

Examples

## completed run-off triangle with the 'unknown' (future) payments
print(triangle <- GFCIB$bodilyInjury[1:15, 1:15])
plot(mcReserve(triangle))

## completed run-off triangle with unknown future
print(observed(triangle))
plot(mcReserve(observed(triangle)))

## the run-off triangle with future payments without MACRAME completion
plot(as.profileLadder(triangle))

Print Objects of the S3 Class mcSetup

Description

Function to organize and print the output provided by the function incrExplor()

Usage

## S3 method for class 'mcSetup'
print(x, ...)

Arguments

Value

displays information resulting from a call of the incrExplor() function

See Also

incrExplor(), mcReserve(), mcBreaks(), mcStates()

Examples

data(CameronMutual)
x <- incrExplor(CameronMutual)
print(x) 

Print Objects of the S3 Class permutedReserve

Description

Function to organize and print the output provided by the permutation bootstrap method implemented in the function permuteReserve()

Usage

## S3 method for class 'permutedReserve'
print(x, ...)

Arguments

Value

Displays information about the estimated reserve (by one of the estimation algorithms – PARALLAX, REACT, or MACRAME) and the overall reserve distribution resulting from a call of the permuteReserve() function

See Also

permuteReserve()

Examples

## reserve point prediction by the PARALLAX method
output <- parallelReserve(CameronMutual)

## reserve distribution prediction by the permutation bootstrap
x <- permuteReserve(output, B = 100)

## summary of the results
print(x) 

Print Objects of the S3 Class profileLadder

Description

Function to organize and print the outputs provided by the function parallelReserve() and the function mcReserve

Usage

## S3 method for class 'profileLadder'
print(x, fancy.print = getOption("profileLadder.fancy", TRUE), ...)

Arguments

Value

displays information resulting from a call of the parallelReserve() function or the mcReserve function

See Also

as.profileLadder(), parallelReserve(), mcReserve()

Examples

data(CameronMutual)
## full run-off triangle printed with the fancy mode
x <- as.profileLadder(CameronMutual)
print(x) 

## run-off triangle with unobserved future payments 
x <- as.profileLadder(observed(CameronMutual))
print(x) 

## the same run-off triangle using a standard printing method 
options(profileLadder.fancy = FALSE)
print(x)

Set Custom Color Styles for profileLadder Output

Description

Function to set user-modified color layout for the run-off triangle visualization and the overall output presentation

Usage

set.fancy.print(
  color.known = "#333333",
  color.predicted = "#CC00CC",
  color.unknown = "#999999",
  color.info = "#CC00CC"
)

Arguments

Value

Sets the user-defined option for fancy print color styles

See Also

print.profileLadder()

Examples

## fancy print option for the run-off triangle 
print(as.profileLadder(observed(CameronMutual)), fancy.print = TRUE)

## standard print option for the run-off triangle
print(as.profileLadder(observed(CameronMutual)), fancy.print = FALSE)

## PARALLAX based run-off triangle completion (fancy print)
options(profileLadder.fancy = TRUE)
parallelReserve(CameronMutual)

## PARALLAX based run-off triangle completion (standard print)
options(profileLadder.fancy = FALSE)
parallelReserve(CameronMutual)

Summary Method for the S3 Class Object mcSetup

Description

The function provides an overall summary of the output from the function incrExplor()

Usage

## S3 method for class 'mcSetup'
summary(object, ...)

Arguments

Value

Returns a standard summary table (with basic description characteristics) for raw run-off triangle increments and their standardized (by using the maximum increment) counterparts. The function also returns the corresponding bins for the increments and their representations in terms of the Markov chain states.

See Also

incrExplor(), mcBreaks(), mcStates()

Examples

data(CameronMutual)
summary(CameronMutual)

## default summary output
summary(incrExplor(CameronMutual))

## summary output for user-modified settings
summary(incrExplor(CameronMutual, states = 5, method = "mean"))

Summary Method for the S3 Objects permutedReserve

Description

The function provides an overall summary of the output from the function permuteReserve() (i.e., the summary of the object of the class permutedReserve)

Usage

## S3 method for class 'permutedReserve'
summary(object, triangle.summary = FALSE, ...)

Arguments

Value

Summary of the completed functional profiles (provided by one of the functions parallelReserve() or mcReserve()) and the overall reserve distribution obtained in terms of the permutation bootstrap – the function permuteReserve(). The output is a list with the following items:

See Also

parallelReserve(), mcReserve(), permuteReserve()

Examples

data(CameronMutual)
summary(CameronMutual)

## summary for the point reserve prediction
summary(parallelReserve(CameronMutual))

## summary for the overall reserve distribution
summary(permuteReserve(parallelReserve(CameronMutual)))

Summary Method for Objects of the S3 Class Method profileLadder

Description

The function provides an overall summary of the output from the functions parallelReserve() and mcReserve() (summary of the object of the class profileLadder)

Usage

## S3 method for class 'profileLadder'
summary(object, plotOption = FALSE, ...)

Arguments

Value

Summary of the completed functional profiles and the estimated reserve (provided by the function parallelReserve() or mcReserve()). Summary of the incremental residuals (standard or backfitted) is also provided if the residuals are available. The output is a list with the following items:

See Also

as.profileLadder(), parallelReserve(), mcReserve()

Examples

data(CameronMutual)
summary(CameronMutual)

## standard summary output
summary(mcReserve(CameronMutual))

## summary output with plotOption = TRUE
summary(mcReserve(CameronMutual), plotOption = TRUE)

## summary output with (standard) residuals and plotOption = TRUE
summary(mcReserve(CameronMutual, residuals = TRUE), plotOption = TRUE)

## summary output with (back-fitted) residuals and plotOption = TRUE
summary(mcReserve(observed(CameronMutual), residuals = TRUE), plotOption = TRUE)

Internet Provider Monthly Income Data

Description

An illustrative dataset—a matrix (of the dimensions 12x12) with a monthly-based income (in EUR) of a local internet data provider with the income structured by the customers subscribing within the given month (in 2023) reported in the rows and monthly-based payments reported in columns. The data matrix represents the incremental type of the run-off triangle.

Usage

data(xNetSubscribe)

Format

xNetSubscribe

A simple 12x12 (trangular) matrix of the class triangle with twelve consecutive months (January 2023 – December 2023) when new customers subscribed to the stream service (rows) and monthly-based payments (columns)