Exploration of Run-Off Triangle Increments

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

triangle: cumulative or incremental run-off triangle (an object of the class triangle or matrix) specified in terms of a partially observed (run-off triangle) or a fully observed (completed triangle) matrix. Only the upper-left triangular part (run-off trangle) is used to provide the output analysis of the incremental payments and the underlying Markov chain setting options
method: method form c("median", "mean", "max", "min") used to summarize the run-off triangle increments within the given set of bins. Each bin with the increments is represented by a corresponding Markov state value (obtained by the method choice with median being the DEFAULT option)
out: integer value ranging from 1 to the number of development periods (alternatively a vector of such integers) to indicate which columns of the run-off triangle should be excluded from the exploratory analysis of the increments. By DEFAULT, the first incremental payments—i.e., the first column of the run-off triangle—are not considered (out = 1). No colums are exluded for out = 0 and the whole run-off triangle is analyzed by incrExplor(). To specify multiple columns that should be excluded, one can use out = c(1,2,3) which will exlude the first three columns (the first three origins respectively) from the exploratory analysis
states: either an integer value to indicate an explicit number of the Markov chain states to be used or a vector of explicit Markov chain states can be provided. The DEFAULT option (states = NULL) ensures a fully data-driven (automatic) set of the Markov chain states as originally proposed in Maciak, Mizera, and Pešta (2022)
breaks: numeric vector of explicit (unique and monotonously increasing) break points to define the bins for the run-off triangle increments. If states is equal to some integer number (i.e., the explicit number of the Markov chain states is requested by states) then the value of breaks is ignored. If both states and breaks are specified (i.e., numeric vectors are provided for both) then the set of states in states must be given in a way that exactly one state value belongs to exactly one bin defined by the break points specified by breaks

Value

An object of the class mcSetup with the following elements:

incrTriangle: an object of the class triangle with the incremental run-off triangle
triangleType: type of the input run-off triangle provided for the input object triangle (cumulative or incremental)
defaultStates: the data-driven set of explicit states as used (by DEFAULT) by the mcReserve() function – the MACRAME prediction algorithm
defaultBreaks: the set of explicit data-driven breaks as used (by DEFAULT) by the mcReserve() function – the MACRAME prediction algorithm
increments: table with basic empirical characteristics of the increments of the input run-off triangle (without the first origin payments—the values in the first column of the run-off triangle). Two sets of increments are provided: the raw incremental payments in the first row of the table and the standardized increments (i.e., row incremental payments divided by the maximum payment within the row (while not considering the columns specified by the out parameter)
userDefined: a list with all information regarding the user modified input (numeric vector increments with the increments being analyzed; numeric value in outColumns denoting the excluded columns in the run-off triangle; method used to summarize the increments within the bins; numeric vector with the resulting Markov chain states in states and the corresponding numeric vector with the break points in breaks defining the bins for the run-off triangle increments)

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

data(CameronMutual) 

## default Markov Chain states with (roughly) equally occupied bins 
incrExplor(CameronMutual)
#> Data-driven (default) setting of the Markov Chain in MACRAME
#> MC States: 13 81 197 302.5 438 601 948 1672.5 3073 3993
#> 
#> Corresponding bins for the run-off triangle increments
#>  [1] "[-Inf, 75)"   "[75, 147)"    "[147, 288)"   "[288, 388)"   "[388, 554)"  
#>  [6] "[554, 780)"   "[780, 1465)"  "[1465, 2587)" "[2587, 3955)" "[3955, Inf)" 
#> 

## five Markov Chain states (with roughly equally occupied bins)
incrExplor(CameronMutual, states = 5)
#> Data-driven (default) setting of the Markov Chain in MACRAME
#> MC States: 13 81 197 302.5 438 601 948 1672.5 3073 3993
#> 
#> Corresponding bins for the run-off triangle increments
#>  [1] "[-Inf, 75)"   "[75, 147)"    "[147, 288)"   "[288, 388)"   "[388, 554)"  
#>  [6] "[554, 780)"   "[780, 1465)"  "[1465, 2587)" "[2587, 3955)" "[3955, Inf)" 
#> 
#> User-modified MC setting
#> MC States: 38 283 529 1371 3216
#> 
#> Corresponding bins for the run-off triangle increments
#> [1] "[-Inf, 147)" "[147, 388)"  "[388, 780)"  "[780, 2587)" "[2587, Inf)"
#> 
#> Development periods (run-off triangle columns) not considered: 1
#> Method selected to summarize the increments within each bin: DEFAULT (median)

## 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))
#> Data-driven (default) setting of the Markov Chain in MACRAME
#> MC States: 13 81 197 302.5 438 601 948 1672.5 3073 3993
#> 
#> Corresponding bins for the run-off triangle increments
#>  [1] "[-Inf, 75)"   "[75, 147)"    "[147, 288)"   "[288, 388)"   "[388, 554)"  
#>  [6] "[554, 780)"   "[780, 1465)"  "[1465, 2587)" "[2587, 3955)" "[3955, Inf)" 
#> 
#> User-modified MC setting
#> MC States: 8.5 248.5 764 1595 3216
#> 
#> Corresponding bins for the run-off triangle increments
#> [1] "[-Inf, 20)"   "[20, 500)"    "[500, 1000)"  "[1000, 2000)" "[2000, Inf)" 
#> 
#> Development periods (run-off triangle columns) not considered: 1
#> Method selected to summarize the increments within each bin: DEFAULT (median)

## 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")
#> Data-driven (default) setting of the Markov Chain in MACRAME
#> MC States: 13 81 197 302.5 438 601 948 1672.5 3073 3993
#> 
#> Corresponding bins for the run-off triangle increments
#>  [1] "[-Inf, 75)"   "[75, 147)"    "[147, 288)"   "[288, 388)"   "[388, 554)"  
#>  [6] "[554, 780)"   "[780, 1465)"  "[1465, 2587)" "[2587, 3955)" "[3955, Inf)" 
#> 
#> User-modified MC setting
#> MC States: 16 439 978 1786 4969
#> 
#> Corresponding bins for the run-off triangle increments
#> [1] "[-Inf, 20)"   "[20, 500)"    "[500, 1000)"  "[1000, 2000)" "[2000, Inf)" 
#> 
#> Development periods (run-off triangle columns) not considered: 1
#> Method selected to summarize the increments within each bin: 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))
#> Data-driven (default) setting of the Markov Chain in MACRAME
#> MC States: 13 81 197 302.5 438 601 948 1672.5 3073 3993
#> 
#> Corresponding bins for the run-off triangle increments
#>  [1] "[-Inf, 75)"   "[75, 147)"    "[147, 288)"   "[288, 388)"   "[388, 554)"  
#>  [6] "[554, 780)"   "[780, 1465)"  "[1465, 2587)" "[2587, 3955)" "[3955, Inf)" 
#> 
#> User-modified MC setting
#> MC States: 10 250 800 1500
#> 
#> Corresponding bins for the run-off triangle increments
#> [1] "[-Inf, 20)"  "[20, 500)"   "[500, 1000)" "[1000, Inf)"
#> 
#> Development periods (run-off triangle columns) not considered: 1
#> Method selected to summarize the increments within each bin: DEFAULT (median)

Usage

Arguments

Value

References

See also

Examples