claim_payment_inflation {SynthETIC}

Size of Partial Payments (With Inflation)

Description

Converts the (compound) list of constant-dollar-value payment sizes to a (compound) list of inflated payment sizes by applying inflation rates on a continuous time scale.

Compare with claim_payment_size() which generates the constant dollar amount of partial payment sizes. Note that the constant dollar values are as of time 0.

Usage

claim_payment_inflation(
  frequency_vector,
  payment_size_list,
  payment_time_list,
  occurrence_list,
  claim_size_list,
  base_inflation_vector,
  si_occurrence_function,
  si_payment_funtion
)

Arguments

frequency_vector

a vector of claim frequencies for all the occurrence periods.

payment_size_list

(compound) list of payment size pattern (without inflation).

payment_time_list

(compound) list of payment times on a continuous time scale.

occurrence_list

(compound) list of occurrence times on a continuous time scale.

claim_size_list

list of claim sizes.

base_inflation_vector

vector showing quarterly base inflation rates (quarterly effective) for all the periods under consideration (default at nil base inflation).

si_occurrence_function

function of occurrence_time and claim_size that outputs the superimposed inflation index with respect to claim occurrence time (see Details for the default inflation function).

si_payment_funtion

function of payment_time and claim_size that outputs the superimposed inflation index with respect to payment time (see Details for the default inflation function).

Details

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

By default we assume

• Nil base inflation.

• No superimposed inflation by (continuous) occurrence time for the first 20 quarters (converted to the relevant time_unit); beyond 20 quarters, the inflation index is given by

  1 - 0.4 max(0, 1 - claim_size/(0.25 * ref_claim))

  where ref_claim is a package-wise global variable that user is required to define at the top of their code using set_parameters. The interpretation is that, due to some external change to the insurance scheme at the end of occurrence quarter 20, the smallest claims will reduce by up to 40% in size. This change will not impact claims exceeding 0.25*ref_claim in size. The reduction varies linearly between these claim sizes.

• Superimposed inflation by (continuous) payment time operates at a period rate of

  \gamma * max(0, 1 - claim_size/ref_claim)

  where \gamma is equivalent to a 30% p.a. inflation rate (converted to the relevant time_unit). The interpretation is that, for claims of small size the payment time superimposed inflation tends to be very high (30% p.a.); whereas for claims exceeding ref_claim in dollar values as of t = 0, the payment time superimposed inflation is nil. The rate of inflation varies linearly between claim sizes of zero and ref_claim.
  
  

Remark on continuous inflation: We note that SynthETIC works with exact transaction times, so time has been measured continuously throughout the program. This allows us to apply inflation on a continous time scale too. For example, we asked the users to provide base inflation as a vector of quarterly base inflation rates, quarterly effective for all the periods under consideration. This data is generally available online (e.g. the Australian quarterly inflation is available on RBA's website - see link). We then interpolate the quarterly inflation rates to compute the addition of inflation by exact times. In the case of above, if we observed quarterly inflation rates of 0.6%, 0.5%, 0.7% and 0.3% for one particular year, then the base inflation applied to a payment at time t = 1.82 quarters will be 1.006 * 1.005^{0.82}.

Remark on out-of-bound payment times: This function includes adjustment for out-of-bound transaction dates, by forcing payments that were projected to fall out of the maximum development period to be paid at the exact end of the maximum development period allowed. For example, if we consider 40 periods of development and a claim incurred in the interval (20, 21] was projected to have a payment at time 62.498210, then we would treat such a payment as if it occurred at time 60 for the purpose of inflation.

Examples

# remove SI occurrence and SI payment
SI_occurrence <- function(occurrence_time, claim_size) {1}
SI_payment <- function(payment_time, claim_size) {1}
# base inflation constant at 0.02 p.a. effective
# (length is 80 to cover the maximum time period)
base_inflation_vector <- rep((1 + 0.02)^(1/4) - 1, times = 80)
attach(test_claims_object)
payment_inflated_list <- claim_payment_inflation(
  frequency_vector, payment_size_list, payment_time_list,
  occurrence_list, claim_size_list, base_inflation_vector,
  SI_occurrence, SI_payment
)
detach(test_claims_object) # undo the attach
# inflated payments for claim 1 of occurrence period 1
payment_inflated_list[[1]][[1]]