claim_majRev {SPLICE}

Major Revisions of Incurred Loss

Description

A suite of functions that works together to simulate, in order, the (1) frequency, (2) time, and (3) size of major revisions of incurred loss, for each of the claims occurring in each of the periods.

Usage

claim_majRev_freq(
  claims,
  rfun,
  paramfun,
  frequency_vector = claims$frequency_vector,
  claim_size_list = claims$claim_size_list,
  ...
)

claim_majRev_time(
  claims,
  majRev_list,
  rfun,
  paramfun,
  claim_size_list = claims$claim_size_list,
  settlement_list = claims$settlement_list,
  payment_delay_list = claims$payment_delay_list,
  ...
)

claim_majRev_size(majRev_list, rfun, paramfun, ...)

Arguments

claims

an claims object containing all the simulated quantities (other than those related to incurred loss), see claims.

rfun

optional alternative random sampling function for:

• claim_majRev_freq: the number of major revisions;

• claim_majRev_time: the epochs of major revisions measured from claim notification;

• claim_majRev_size: the sizes of the major revision multipliers.

See Details for default.

paramfun

parameters for the random sampling function, as a function of other claim characteristics such as claim_size; see Details.

frequency_vector

a vector of claim frequencies for all the periods (not required if the claims argument is provided); see claim_frequency.

claim_size_list

list of claim sizes (not required if the claims argument is provided); see claim_size.

...

other arguments/parameters to be passed onto paramfun.

majRev_list

nested list of major revision histories (with non-empty revision frequencies).

settlement_list

list of settlement delays (not required if the claims argument is provided); see claim_closure.

payment_delay_list

(compound) list of inter partial delays (not required if the claims argument is provided); see claim_payment_delay.

Value

A nested list structure such that the jth component of the ith sub-list is a list of information on major revisions of the jth claim of occurrence period i. The "unit list" (i.e. the smallest, innermost sub-list) contains the following components:

majRev_freq	Number of major revisions of incurred loss [claim_majRev_freq()].
majRev_time	Time of major revisions (from claim notification) [claim_majRev_time()].
majRev_factor	Major revision multiplier of incurred loss [claim_majRev_size()].
majRev_atP	An indicator, 1 if the last major revision occurs at the time of the last major payment (i.e. second last payment), 0 otherwise [claim_majRev_time()].

Details - claim_majRev_freq (Frequency)

Let K represent the number of major revisions associated with a particular claim. The notification of a claim is considered as a major revision, so all claims have at least 1 major revision (K \ge 1).

The default majRev_freq_function specifies that no additional major revisions will occur for claims of size smaller than or equal to claim_size_benchmark (0.075 * ref_claim by default). For claims above this threshold,

Pr(K = 2)	= 0.1 + 0.3min(1, (claim_size - 0.075 * ref_claim) / 0.925 * ref_claim)
Pr(K = 3)	= 0.5min(1, max(0, claim_size - 0.25 * ref_claim)/ (0.75 * ref_claim))
Pr(K = 1)	= 1 - Pr(K = 2) - Pr(K = 3)

where ref_claim is a package-wise global variable that user should define by set_parameters (if moving away from the default).

The idea is that major revisions are more likely for larger claims, and do not occur at all for the smallest claims. Note also that by default a claim may experience up to a maximum of 2 major revisions in addition to the one at claim notification. This is taken as an assumption in the default setting of claim_majRev_size(). If user decides to modify this assumption, they will need to take care of the part on the major revision size as well.

Details - claim_majRev_time (Time)

Let \tau_k represent the epoch of the kth major revision (time measured from claim notification), k = 1, ..., K. As the notification of a claim is considered a major revision itself, we have \tau_1 = 0 for all claims.

The last major revision for a claim may occur at the time of the second last partial payment (which is usually the major settlement payment) with probability

0.2 min(1, max(0, (claim_size - ref_claim) / (14 * ref_claim)))

where ref_claim is a package-wise global variable that user should define by set_parameters (if moving away from the default).

Now, if there is a major revision at the time of the second last partial payment, then \tau_k, k = 2, ..., K - 1 are sampled from a triangular distribution with parameters (see also ptri)

• min = time_to_second_last_payment / 3

• max = time_to_second_last_payment

• maximum density at mode = time_to_second_last_payment / 3.

Otherwise (i.e. no major revision at the time of the second last partial payment), \tau_k, k = 2, ..., K are sampled from a triangular distribution with parameters

• min = settlement_delay / 3

• max = settlement_delay

• maximum density at mode = settlement_delay / 3.

Note that when there is a major revision at the time of the second last partial payment, majRev_atP (one of the output list components) will be set to be 1.

Details - claim_majRev_size (Revision Multiplier)

As mentioned in the frequency section ("Details - claim_majRev_freq"), the default function for the major revision multipliers assumes that there are only up to 2 major revisions (in addition to the one at claim notification) for all claims.

By default,

• the first major revision multiplier g_1 is simply 1 (no meaning);

• the second major revision multiplier g_2 is sampled from a lognormal distribution with parameters meanlog = 1.8 and sdlog = 0.2;

• the third major revision multiplier g_3 is sampled from a lognormal distribution with parameters meanlog = 1 + 0.07(6 - g_2) and sdlog = 0.1. Note that the third major revision is likely to be smaller than the second.

The revision multipliers are subject to further constraints to ensure that the revised incurred estimate never falls below what has already been paid. This is dicussed in claim_history.

The major revision multipliers apply to the incurred loss estimates, that is, a revision multiplier of 2.54 means that at the time of the major revision the incurred loss increases by a factor of 2.54. We highlight this as in the case of minor revisions, the multipliers will instead apply to outstanding claim amounts, see claim_minRev.

See Also

claims

Examples

set.seed(1)
test_claims <- SynthETIC::test_claims_object
major <- claim_majRev_freq(test_claims)
major[[1]][[1]] # the "unit list" for the first claim

# update the timing information
major <- claim_majRev_time(test_claims, major)
# observe how this has changed
major[[1]][[1]]

# update the revision multipliers
major <- claim_majRev_size(major)
# again observe how this has changed
major[[1]][[1]]