claim_payment_size: Size of Partial Payments (Without Inflation) In SynthETIC: Synthetic Experience Tracking Insurance Claims

 claim_payment_size R Documentation

Size of Partial Payments (Without Inflation)

Description

Simulates and returns the constant dollar amount of each partial payment (i.e.without inflation) for each of the claims occurring in each of the periods.

Usage

``````claim_payment_size(
frequency_vector,
claim_size_list,
no_payments_list,
rfun,
paramfun,
...
)
``````

Arguments

 `frequency_vector` a vector of claim frequencies for all the periods. `claim_size_list` list of claim sizes. `no_payments_list` list of number of partial payments. `rfun` optional alternative random sampling function; see Details for default. `paramfun` parameters for the random sampling function, as a function of `claim_size`; see Details. `...` other arguments/parameters to be passed onto `paramfun`.

Details

Returns a compound list structure such that the `j`th component of the `i`th sub-list gives the payment pattern (as a vector) for the `j`th claim of occurrence period `i`.

The default `rfun` is set up in three steps. First we sample the complement of the proportion of total claim size represented by the last two payments, from a Beta distribution with mean

`1 - min(0.95, 0.75 + 0.04log[claim_size/(0.10 * ref_claim)])`

where `ref_claim` is a package-wise global variable that we ask the user to define at the top of their code using `set_parameters`. CoV is assumed constant at 20%.

Next we simulate the proportion of last_two_pmts paid in the second last payment (settlement of the claim) from a Beta distribution with mean = 0.90 and CoV = 3%.

Lastly we sample the remaining payment proportions from a Beta distribution with mean

`(1 - last_two_payments)/(no_pmt - 2)`

and CoV = 10%, which is followed by a normalisation such that the proportions add up to 1.

In the cases where there are only 2 or 3 partial payments, proceed as if there were 4 or 5 payments respectively with last_two_payments = 0. The trivial case is when the claim is settled with a single payment, which must be of the same amount as the total claim size.

Alternative sampling distributions are supported through `rfun` (the random generation function) and `paramfun` (which returns the parameters of `rfun` as a function of `claim_size`). The `paramfun` should return the distribution parameters in a vector, e.g. for gamma distribution `paramfun` should return a value in the format of `c(shape = , scale = )`. If a `rfun` is specified without a `paramfun`, `SynthETIC` will try to proceed without parameterisation (i.e. directly calling `rfun` with `claim_size`), and if it fails, then return an error message.

Explanation

Why did we set up a payment pattern as above?

The payment pattern is set up to reflect the typical pattern of a claim from an Auto liability line of business, which usually consists of:

1. (possibly) some small payments such as police reports, medical consultations and reports;

2. some more substantial payments such as hospitalisation, specialist medical procedures, equipment (e.g. prosthetics);

3. a final settlement with the claimant (usually the second last payment);

4. a smaller final payment, usually covering legal costs.

Claims in a number of other lines of business exhibit a similar structure, albeit with possible differences in the types of payment made.

Examples

``````# set up
n_vector <- claim_frequency(I = 10)
claim_sizes <- claim_size(n_vector)
no_payments <- claim_payment_no(n_vector, claim_sizes)

# with default rfun
payments <- claim_payment_size(n_vector, claim_sizes, no_payments)
# partial payment sizes for claim 1 of occurrence period 1
payments[[1]][[1]]

# with some custom rfun
# simplistic case: (stochastically) equal amounts
my_func <- function(n, claim_size) {
prop <- runif(n)
prop <- prop / sum(prop)
claim_size * prop
}
mypayments <- claim_payment_size(n_vector, claim_sizes, no_payments, my_func)
# partial payment sizes for claim 1 of occurrence period 1
mypayments[[1]][[1]]
``````

SynthETIC documentation built on May 29, 2024, 8:47 a.m.