claim_history: Development of Case Estimates

In SPLICE: Synthetic Paid Loss and Incurred Cost Experience (SPLICE) Simulator

Development of Case Estimates

Description

Consolidates payments and incurred revisions and returns a full transactional history of all the individual claims (transaction being either a payment or a case estimate revision).

Usage

claim_history(
  claims,
  majRev_list,
  minRev_list,
  k1 = 0.95,
  k2 = 0.95,
  base_inflation_vector = NULL,
  keep_all = FALSE
)

Arguments

claims	an claims object containing all the simulated quantities (other than those related to incurred loss), see claims.
majRev_list	nested list of major revision histories, see claim_majRev.
minRev_list	nested list of minor revision histories, see claim_minRev.
k1	maximum amount of cumulative claims paid as a proportion of total incurred estimate for major revisions; between 0 and 1.
k2	maximum amount of cumulative claims paid as a proportion of total incurred estimate for minor revisions; between 0 and 1.
base_inflation_vector	vector showing quarterly base inflation rates (quarterly effective) for all the periods under consideration (default is nil base inflation), should be consistent with the input inflation vector in claim_payment_inflation. If a single number is provided, the function will assume constant quarterly inflation.
keep_all	TRUE to keep the paid, outstanding payments, total incurred estimates just before the revision, FALSE to keep only the estimates right after the revision (⁠_right⁠).

Details

This function works to generate the full history of claims paid and incurred estimates by consolidating all the simulated revision quantities. It should be noted that in this consolidation step, we make the following adjustments:

• Major and minor revisions should not occur simultaneously. In the event that they do (which is only possible at the second last partial payment), the major revision takes precedence, and the minor revision be discarded. This will be reflected in the majRev and minRev components of the output list.

• Estimates of incurred loss are specified to be computed in reverse order, and it is necessary that the total incurred estimate is always strictly greater than the cumulative claims paid (except at the final paymen where equality holds). Hence we introduce k1 and k2 to make sure that the revised incurred estimates satisfy

  ky(t) \ge c(t)

  where y(t) represents the total incurred estimate at delay t, k is a constant between 0 and 1, and c(t) is the cumulative claims paid up to time t. When the raw simulated revision multipliers violate this requirement, the case estimates of the total incurred or the outstanding claim payments will be increased to make sure this condition always holds, i.e. this adjustment takes precedence over the raw simulated revision multipliers.

• Inflation adjustment: One can choose to ignore inflation in the incurred estimates (default), or to make allowance for it.

  • If base_inflation_vector == NULL (default), then all case estimates will be computed in values corresponding to time t = 0, i.e. the commencement of the first occurrence period.

  • If base_inflation_vector is provided, then the case estimators will include full superimposed inflation and base inflation only up to the date of the revision, i.e. there is an adjustment for the time elapsed since the immediately preceding revision and no future base inflation beyond the date of valuation.

  • If inflation is involved, it should be noted that the case estimator reviews the base inflation situation only in the process of making a revision. When only a payment is made, the insurer's system automatically writes down the outstanding liability on the assumption of no change in ultimate incurred amount.

Value

A nested list structure such that the jth component of the ith sub-list provides a full transactional history of the jth claim of occurrence period i. The "unit list" (i.e. the smallest, innermost sub-list) contains the following components:

txn_delay	Delays from notification to the transactions (payment or incurred revision).
txn_time	Times of the transactions (from the commencement of the first occurrence period).
txn_type	Types of the transactions, "Ma" for major revision, "Mi" for minor revision, "P" for payment, "PMa" for major revision coincident with a payment, "PMi" for minor revision coincident with a payment.
cumpaid_right	Cumulative claim payments immediately after each of the transactions (in the "right" continuous sense).
OCL_right	Case estimate of outstanding claim payments immediately after each of the transactions (in the "right" continuous sense).
incurred_right	Case estimate of incurred loss immediately after each of the transactions (in the "right" continuous sense).
minRev	A list containing full history of minor revisions (frequency, time and revision size); claim_minRev.
majRev	A list containing full history of major revisions (frequency, time and revision size); see claim_majRev.

and optionally (by setting keep_all = TRUE),

cumpaid_left	Cumulative claim payments just before each of the transactions.
OCL_left	Case estimate of outstanding claim payments just before each of the transactions.
incurred_left	Case estimate of incurred loss just before each of the transactions.

SPLICE documentation built on April 16, 2023, 9:19 a.m.