In jimbrig/lossrx: Actuarial Loss Development and Reserving with R

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  message = FALSE,
  warning = FALSE,
  error = FALSE,
  results = "asis"
)

library(lossrx)
library(dplyr)
library(purrr)
library(knitr)
library(kableExtra)
library(lubridate)
library(dbplyr)
library(janitor)
library(summarytools)

Overview

A lossrun is an insurance/actuarial term for a dataset containing information about a particular insurance coverage or policy's individual claims as of a particular point in time known as the evaluation date.

lossrx provides examples and support functions to aid in the creation, analysis, validation, and proper storage of actuarial lossruns specific to P&C Insurance Coverages.

Coverages

It is important to note the granularity of a particular lossrun with regard to what level of detail its values represent as well as the context in which the data is provided from.

For example, it is common to have separate lossruns by coverage due to the differences in the attributable dimensions associated with the values in those lossruns by coverage.

For example, a Worker's Compensation lossrun will typically split its values for paid, case reserves, and incurred/reported into lower-level spit-outs by:

Indemnity
Medical
Expense

Whereas, in Automobile Insurance Coverages the claim amounts would be split out between

Bodily Injury (BI)
Property Damage
Expense

lossrx supports analysis for the following Property Casualty coverages:

Workers Compensation - WC
Automobile Liability - AL
General Liability - GL
Medical Professional Liability - MPL (Hospitals and Physicians)
Other Various Liability Types similar to WC, AL, and GL (i.e. property, government, etc.)

Different coverages have different types of fields in their respective lossruns which is discussed in detail in the coverages vignette.

Typical Lossrun Fields

Each row in a lossrun should correspond to a specific claim at a specific point in time.

The following fields are typical in all lossruns, regardless of coverage of business context:

Key Fields:
Unique Claim ID
Occurrence ID (for claims related to a single accident that are grouped by occurrence)
Claimant Name (First, Last, etc.)
Other Claimant Information (Age, Gender, Tenure, etc.)
Policy Details (Retention Limits, Deductibles, Reinsurance Thresholds, Aggregate Thresholds, ALAE Treatment, etc.)
Dates
Evaluation Date of the Lossrun
Date of Accident / Loss
Date of Report
Report Lag { Report Date - Loss Date } (Calculated)
Close Date(s)
Re-open Date(s)
Hire Date (for employee)
Birth Date (for claimant - to derive Age)
Claim Information Fields
Claim Status
Claim Type (Indemnity, Medical Only, Closed no Pay, etc.)
Litigation (Boolean)
Location (Accident, Claimant, Jurisdiction)
Numeric Financial Fields
Total Unlimited Reported / Incurred
Total Unlimited Paid
Total Unlimited Reserve
Various Splits depending on Coverage
- Indemnity, Medical, Expense
- Bodily Injury, Property Damage, Expense
- Physician, Hospital, etc.
Recoveries, Subrogation, etc.

Example Lossrun

lossrx provides example lossruns in the form of a merged dataset named losses.

loss_data <- losses
dplyr::glimpse(loss_data)

Note that the losses dataset contains r length(unique(loss_data$eval_date)) unique evaluation dates merged together:

analysis_data_wc <- loss_data |>
  filter(coverage == "WC") |>
  group_by(.data$eval_date, .data$devt_age, .data$program_year) |>
  summarise(
    `Total Reported Claim Counts` = n(),
    `Total Paid` = sum(.data$total_paid, na.rm = TRUE),
    `Total Reported` = sum(.data$total_incurred, na.rm = TRUE)
  ) |>
  ungroup() |>
  arrange(program_year, devt_age)

This can easily be translated into triangles like so:

create_triangle <- function(dat, type = c("paid", "reported", "counts")) {

  col <- switch(type,
                "paid" = "Total Paid",
                "reported" = "Total Reported",
                "counts" = "Total Reported Claim Counts")

  dat |>
    dplyr::filter(.data$devt_age %% 12 == 0) |>
    dplyr::select(.data$program_year, .data$devt_age, col) |>
    tidyr::pivot_wider(
      names_from = .data$devt_age,
      values_from = col
    )

}

wc_tris <- purrr::map(c("Paid Triangle" = "paid",
                        "Reported Triangle" = "reported",
                        "Reported Claim Counts Triangle" = "counts"),
                      ~create_triangle(dat = analysis_data_wc, .x))

Triangles

Reported Triangle for Worker's Compensation

wc_tris[["Reported Triangle"]] |>
  rename(`Program Year` = program_year) |>
  mutate_at(vars(2:10), formattable::currency, digits = 0) |>
  kable(
    digits = 0, 
    align = "c", 
    caption = "Reported Loss Triangle - Worker's Compensation",
    format.args = list(big.mark = ",")
  ) |>
  kableExtra::kable_styling()

Paid Triangle for Worker's Compensation

wc_tris[["Paid Triangle"]] |>
  rename(`Program Year` = program_year) |>
  mutate_at(vars(2:10), formattable::currency, digits = 0) |>
  kable(
    digits = 0, 
    align = "c", 
    caption = "Paid Loss Triangle - Worker's Compensation",
    format.args = list(big.mark = ",")
  ) |>
  kableExtra::kable_styling()

Reported Claim Counts Triangle for Worker's Compensation

wc_tris[["Reported Claim Counts Triangle"]] |>
  rename(`Program Year` = program_year) |>
  mutate_at(vars(2:10), formattable::comma, digits = 0) |>
  kable(
    digits = 0, 
    align = "c", 
    caption = "Reported Claim Counts Triangle - Worker's Compensation",
    format.args = list(big.mark = ",")
  ) |>
  kableExtra::kable_styling()