PiecewisePareto_Layer_Mean: Layer Mean of the Piecewise Pareto Distribution

In Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

Layer Mean of the Piecewise Pareto Distribution

Description

Calculates the expected loss of a piecewise Pareto distribution in a reinsurance layer

Usage

PiecewisePareto_Layer_Mean(
  Cover,
  AttachmentPoint,
  t,
  alpha,
  truncation = NULL,
  truncation_type = "lp"
)

Arguments

Cover	Numeric. Cover of the reinsurance layer.
AttachmentPoint	Numeric. Attachment point of the reinsurance layer.
t	Numeric vector. Thresholds of the piecewise Pareto distribution.
alpha	Numeric vector. alpha[i] is the Pareto alpha in excess of t[i].
truncation	Numeric. If truncation is not NULL and truncation > t, then the Pareto distribution is truncated at truncation.
truncation_type	Character. If truncation_type = "wd" then the whole distribution is truncated. If truncation_type = "lp" then a truncated Pareto is used for the last piece.

Value

The expected loss of the (truncated) piecewise Pareto distribution with parameter vectors t and alpha in the layer Cover xs AttachmentPoint

References

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

Examples

t <- c(1000, 2000, 3000)
alpha <- c(1, 1.5, 2)
PiecewisePareto_Layer_Mean(4000, 1000, t, alpha)
PiecewisePareto_Layer_Mean(4000, 1000, t, alpha, truncation = 5000)
PiecewisePareto_Layer_Mean(4000, 1000, t, alpha, truncation = 5000, truncation_type = "lp")
PiecewisePareto_Layer_Mean(4000, 1000, t, alpha, truncation = 5000, truncation_type = "wd")

Pareto documentation built on April 18, 2023, 9:10 a.m.