SynthETIC (version 1.1.0)

claim_notification: Claim Notification

Description

Simulates and returns the notification/reporting delays of each of the claims occurring in each of the periods, according to a user-specified distribution (by default a Weibull).

Usage

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

Value

A list of notification delays such that the \(i\)th component of the list gives the notification delays for all claims that occurred in period \(i\).

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; if not specified, assumes Weibull.

paramfun

parameters for the random sampling function, as a function of claim_size and occurrence_period; see Details.

...

other arguments/parameters to be passed onto paramfun.

Details

Claim notification delay represents the delay from claim occurrence to reporting. SynthETIC assumes the (removable) dependence of notification delay on claim size and occurrence period of the claim, thus requiring the user to specify a paramfun of claim_size and occurrrence_period (with the option to add more arguments as needed).

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 = ), for exponential distribution this should return c(rate = ). See Examples. If a rfun is specified without a paramfun, SynthETIC will try to proceed without parameterisation (i.e. directly calling rfun with claim size and occurrence period), and if it fails, return an error message.

By default, it is assumed that the notification delay follows a Weibull distribution, and that the mean notification delay (in quarters) is given by $$min(3, max(1, 2-[log(claim_size/(0.50*ref_claim))]/3))$$ automatically converted to the relevant time_unit defined by user at the top of their script through set_parameters. Note that the ref_claim in the equation is another package-wise global variable that the user needs to define through set_parameters as it determines the monetary scale of the simulator. The CoV (Coefficient of Variation) of the notification delay is assumed to be constant at 70%, independent of the size and occurrence period of the claim.

Of course, the user may wish to sample from a different distribution rfun and/or a different set of parameters. An example is given below.

Examples

n_vector <- c(90, 79, 102, 78, 86, 88, 116, 84, 93, 104)

# Try a constant Weibull distribution
# (i.e. independent of claim size and occurrence period)
notidel_param <- function(claim_size, occurrence_period) {
  mean <- 2; cv <- 0.70
  shape <- get_Weibull_parameters(mean, cv)[1, ]
  scale <- get_Weibull_parameters(mean, cv)[2, ]
  c(shape = shape, scale = scale)
}

notidel <- claim_notification(n_vector, claim_size(n_vector),
                              paramfun = notidel_param)
notidel[[1]] # show notification for claims originating from period 1