PiecewisePareto_Layer_Mean function

Layer Mean of the Piecewise Pareto Distribution

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

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.

Returns

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

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")

References

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