Pareto_Extrapolation {Pareto}

Pareto Extrapolation

Description

Uses a Pareto distribution to derive the expected loss of a layer from the expected loss of another layer

Usage

Pareto_Extrapolation(
  Cover_1,
  AttachmentPoint_1,
  Cover_2,
  AttachmentPoint_2,
  alpha,
  ExpLoss_1 = NULL,
  truncation = NULL
)

Arguments

Cover_1

Numeric. Cover of the layer from which we extrapolate. Use Inf for unlimited layers.

AttachmentPoint_1

Numeric. Attachment point of the layer from which we extrapolate.

Cover_2

Numeric. Cover of the layer to which we extrapolate. Use Inf for unlimited layers.

AttachmentPoint_2

Numeric. Attachment point of the layer to which we extrapolate.

alpha

Numeric. Pareto alpha used for the extrapolation.

ExpLoss_1

Numeric. Expected loss of the layer from which we extrapolate. If NULL (default) then the function provides only the ratio between the expected losses of the layers.

truncation

Numeric. If truncation is not NULL and truncation > AttachmentPoint_1, then the Pareto distribution is truncated at truncation.

Value

The expected loss of the layer Cover_2 xs AttachmentPoint_2 given that Cover_1 xs AttachmentPoint_1 has expected loss ExpLoss_1 and assuming a (truncated) Pareto distribution with parameters t and alpha. If missing then ExpLoss_1 == 1 is assumed.

References

Riegel, U. (2018) Matching tower information with piecewise Pareto. European Actuarial Journal 8(2): 437–460

Examples

Pareto_Extrapolation(1000, 1000, 2000, 2000, 2, ExpLoss_1 = 100)
Pareto_Extrapolation(1000, 1000, 2000, 2000, 2) * 100
Pareto_Extrapolation(1000, 1000, 2000, 2000, 2, truncation = 5000, ExpLoss_1 = 100)
Pareto_Extrapolation(1000, 1000, 2000, 2000, 2, truncation = 5000) * 100