mcReserve: 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
)

Value

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

reserve: numeric vector with four values: Total paid amount (i.e., the sum of the last observed diagonal in a cumulative run-off triangle); Estimated ultimate (i.e., the sum of the last column in the completed cumulative run-off triangle); Estimated reserve (i.e., the sum of the last column in the completed cumulative triangle minus the sum of the last observed diagonal in chainLadder); True reserve if a completed chainLadder is provided for the input (i.e., the sum of the last column in chainLadder minus the sum of the last diagonal in chainLadder)
method: algorithm used for the reserve estimation
Triangle: the input run-off triangle provided in chainLadder
FullTriangle: completed run-off triangle (the upper-left triangular part is identical with the input triangle in chainLadder and the lower-right trianglular part is completed by the MACRAME algorithm
trueCompleted: true completed triangle (if available) where the upper-left part is used by the MACRAME algorithm to estimate the reserve and the lower-right part is provided for some evaluation purposes. If the full triangle is not available NA is returned instead
residuals: a triangle with the corresponding residuals (for residuals = TRUE). The residuals are either provided in the upper-left triangle (so-called back-fitted incremental residuals if true completed triangle is not available) or the residuals are given in the lower-right triangle (i,e., standard incremental residuals---if the true completed triangle is given)

Arguments

chainLadder

a cumulative or incremental run-off triangle (the triangle must be of the class triangle or matrix) in terms of a square matrix with a fully observed upper-left triangular part. If the lower-right part is also provided the function will also return standard residuals but only the upper-left (run-off) triangle is be used for the reserve prediction purposes

cum

logical to indicate the type of the input triangle that is provided (DEFAULT value is TRUE for the cumulative triangle, FALSE if chainLadder is of the incremental type)

residuals

logical to indicate whether (incremental) residuals should be provided in output or not. If the run-off triangle is completely observed then the residuals are obtained in terms of the true increments minus the predicted ones. If the bottom-right triangle is not available (which is a typical situation in practice) then the residuals are obtained in terms of a back-fitting approach (see Maciak, Mizera, and Pešta (2022) for further details). However, the back-fitted residuals are only calculated when no user specification of the states (in states) and breaks (in breaks) is provided (as it is usually not appropriate to use the same states/breaks for the flipped run-off triangle)

states

numeric value to provide either the number of the Markov states to be used or it can specify an explicit set of the states instead. The default setting (states = NULL) provides the set of states in a fully data-driven manner as proposed in Maciak, Mizera, and Pešta (2022) while any choice of breaks is ignored. If the number of states is specified by states, the states are obtained analogously as in Maciak, Mizera, and Pešta (2022), however, the number of actual states is adjusted and the parameter breaks is again ignored

If parameter states provides an explicit vector of Markov chain states (the smallest state should be larger than the smallest observed increment in the run-off triangle and, similarly, the largest state should be smaller than the largest observed increment) then the corresponding bins (breaks) for the run-off triangle increments are defined automatically by the midpoints between the provided states (with breaks being set to NULL DEFAULT)

breaks

vector parameter which provides explicit (unique and monotonly increasing) break points (disjoint bins) for the run-off triangle incremenets. Each bin should be represented by the corresponding Markov chain state---either the values given in states or provided automatically if states is not a valid vector of the Markov states. If the breaks are provided as breaks = c(-Inf, ... , Inf) defining k bins all together then states should be a vector of the same length k. Alternatively, the breaks can be also specified by a set of finite numbers defining again k bins---in such cases, the parameter states should be of the length length(states) = k + 1. Each value in states should represent one bin defined by breaks

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

Examples

Run this code

## 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))