Inflate a Triangle based on an Inflation Rate

Inflate the amounts of a Triangle from the latest diagonal based on an Inflation Rate

Usage

inflateTriangle(Triangle, rate)

Arguments

Triangle

claim triangle. Assume columns are the development period, use transpose otherwise. A (mxn)-matrix \(C_{ik}\) which is filled for \(k \leq n+1-i; i=1,\ldots,m; m\geq n \), see qpaid for how to use (mxn)-development triangles with m<n, say higher development period frequency (e.g quarterly) than origin period frequency (e.g accident years).

rate

Inflation rate to be applied to the triangle according to an exponential model

Details

The sensitivity of projections of ultimate losses based on incurred loss development factors to changes in the adequacy level of case reserves increases significantly for the long-tail lines. In particular, if the adequacy of the case reserve is changing, the estimates of ultimate losses based on reported claims could be severely distorted. The function deflates the amounts of latest diagonal to each diagonal of the triangle according to the inflation rate provided, considering an exponential model. The purpose of restating the amounts is to have each diagonal in the triangle at the same level as the latest diagonal (i.e. latest valuation). Ideally the metrics that should be restated are average O/S or average claim paid.

Value

inflateTriangle returns the inflated triangle according to the provided rate

References

Berquist, J.R. and Sherman, R.E., Loss Reserve Adequacy Testing: A Comprehensive, Systematic Approach, Proceedings of the Casualty Actuarial Society, LXIV, 1977, pp.123-184.

Author

Marco De Virgilis devirgilis.marco@gmail.com

See also

See also qpaid for dealing with non-square triangles, checkTriangleInflation to check Y-o-Y Triangle Inflation Rates,

Examples

# Create a Triangle of Average Case O/S

avg <- MedMal$MedMalOutstanding / MedMal$MedMalOpen

# Select a rate of 15% and inflate the average =/S Triangle

inflated_tr <- inflateTriangle(Triangle = avg, rate = .15) 

# Multiply it by open claims and add paymnets to calulate the adjusted Reported Claims Trinagle

adj_reported <- inflated_tr * MedMal$MedMalOpen + MedMal$MedMalPaid

# Calculate the IBNR from the unadjusted Triangle

std_ibnr <- summary(MackChainLadder(MedMal$MedMalReported))$Totals[4, 1]

# Calculate the IBNR from the adjusted Triangle

adj_reported_ibnr <- summary(MackChainLadder(adj_reported))$Totals[4, 1]

# Compare the two

std_ibnr - adj_reported_ibnr
#> [1] 321739113