Distortion risk measure — distortion • prospicio

A concave distortion g of the survival function, giving the coherent risk measure rho(X) = integral of g(S(x)) dx. Every kind has a parameter value (or limit) that gives the mean.

Usage

distortion(
  kind = c("tvar", "wang", "proportional_hazard", "dual_power", "exponential"),
  param
)

Arguments

kind: One of "tvar", "wang", "proportional_hazard", "dual_power" and "exponential".
param: The distortion's parameter.

Value

A distortion object with kind and param properties. Use it with risk_measure() and allocate().

Details

`kind`	`g(s)`	`param`
`"tvar"`	`min(s / (1 - p), 1)`	`p` in `[0, 1]`
`"wang"`	`pnorm(qnorm(s) + lambda)`	`lambda >= 0`
`"proportional_hazard"`	`s^rho`	`rho` in `(0, 1]`
`"dual_power"`	`1 - (1 - s)^beta`	`beta >= 1`
`"exponential"`	`(1 - exp(-k s)) / (1 - exp(-k))`	`k > 0`

The exponential kind is the spectral measure with exponential risk aversion; it gives the mean only in the limit k -> 0.

Examples

d <- distortion("wang", 0.5)
risk_measure(sampled(c(10, 20, 30, 40, 50)), d)
#> [1] 36.48249
distortion_g(distortion("dual_power", 2), 0.3)
#> [1] 0.51