SynthETIC (version 1.1.0)

claim_payment_no: Number of Partial Payments

Description

Simulates and returns the number of partial payments required to settle each of the claims occurring in each of the periods.

Usage

claim_payment_no(frequency_vector, claim_size_list, rfun, paramfun, ...)

Arguments

frequency_vector

a vector of claim frequencies for all the periods.

claim_size_list

list of claim sizes.

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, e.g. if going with the default sampling distribution, you can specify a claim_size_benchmark_1 (below which claims are assumed to be settled with 1 or 2 payments) and claim_size_benchmark_2 (below which claims are assumed to be settled with 2 or 3 payments).

Details

Returns a list structure such that the \(i\)th component of the list gives the number of partial payments required to settle each of the claims that occurred in period \(i\). It is assumed that at least one payment is required i.e. no claims are settled without any single cash payment.

Let \(M\) represent the number of partial payments associated with a particular claim. The default simulate_no_pmt_function is set up such that if claim_size \(\le\) claim_size_benchmark_1, $$Pr(M = 1) = Pr(M = 2) = 1/2;$$ if claim_size_benchmark_1 < claim_size \(\le\) claim_size_benchmark_2, $$Pr(M = 2) = 1/3, Pr(M = 3) = 2/3;$$ if claim_size > claim_size_benchmark_2 then \(M\) is geometric with minimum 4 and mean $$min(8, 4 + log(claim_size/claim_size_benchmark_2)).$$

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.

Examples

n_vector <- claim_frequency(I = 10)
# with default simulation function
no_payments <- claim_payment_no(n_vector, claim_size(n_vector))
no_payments[[1]] # number of payments for claims incurred in period 1

# modify the lower benchmark value
claim_payment_no(n_vector, claim_size(n_vector),
                 claim_size_benchmark_1 = 5000)