stress_RM_mean_sd_w: Stressing Risk Measure, Mean and Standard Deviation
In spesenti/SWIM: Scenario Weights for Importance Measurement

Description Usage Arguments Details Value Author(s) References See Also Examples

Provides weights on simulated scenarios from a baseline stochastic model, such that a stressed model component (random variable) fulfils a constraint on its mean, standard deviation, and risk measure defined by a gamma function and evaluated at a given level alpha. Scenario weights are selected by constrained minimisation of the Wasserstein distance to the baseline model.

stress_RM_mean_sd_w(
  x,
  alpha = 0.8,
  new_means,
  new_sd,
  q_ratio = NULL,
  q = NULL,
  k = 1,
  h = 1,
  gamma = NULL,
  names = NULL,
  log = FALSE,
  method = "Nelder-Mead",
  ...
)

`x`	A vector, matrix or data frame containing realisations of random variables. Columns of `x` correspond to random variables; OR A `SWIMw` object, where `x` corresponds to the underlying data of the `SWIMw` object. The stressed random component is assumed continuously distributed.
`alpha`	Numeric, vector, the level of the Expected Shortfall. (`default Expected Shortfall`)
`new_means`	Numeric, the stressed mean.
`new_sd`	Numeric, the stressed standard deviation.
`q_ratio`	Numeric, vector, the ratio of the stressed RM to the baseline RM (must be same length as `alpha`).
`q`	Numeric, vector, the stressed RM at level `alpha` (must be same length as `alpha`).
`k`	Numeric, the column of `x` that is stressed `(default = 1)`.
`h`	Numeric, a multiplier of the default bandwidth using Silverman’s rule (default `h = 1`).
`gamma`	Function of one variable, that defined the gamma of the risk measure. (`default Expected Shortfall`).
`names`	Character vector, the names of stressed models.
`log`	Boolean, the option to print weights' statistics.
`method`	The method to be used in [stats::optim()]. (`default = Nelder-Mead`).
`...`	Additional arguments to be passed to `nleqslv`.

This function implements stresses on distortion risk measures. Distortion risk measures are defined by a square-integrable function gamma where

\int_0^1 gamma(u) du = 1.

The distortion risk measure for some gamma and distribution G is calculated as:

ρ_{gamma}(G) = \int_0^1 \breve(G)(u) gamma(u) du.

Expected Shortfall (ES) is an example of a distortion risk measure. The ES at level alpha of a random variable with distribution function F is defined by:

ES_{alpha} = 1 / (1 - alpha) * \int_{alpha}^1 VaR_u d u.

A SWIMw object containing:

x, a data.frame containing the data;
h, h is a multiple of the Silverman’s rule;
u, vector containing the gridspace on [0, 1];
lam, vector containing the lambda's of the optimized model;
str_fY, function defining the densities of the stressed component;
str_FY, function defining the distribution of the stressed component;
str_FY_inv, function defining the quantiles of the stressed component;
gamma, function defining the risk measure;
new_weights, a list of functions, that applied to the kth column of x, generates the vectors of scenario weights. Each component corresponds to a different stress;
type = "RM mean sd";
specs, a list, each component corresponds to a different stress and contains k, alpha, q, new_means, and new_sd.

See SWIM for details.

Zhuomin Mao

\insertRef

Pesenti2019reverseSWIM

\insertRef

Pesenti2020SSRNSWIM

\insertRef

Pesenti2021SSRNSWIM

Other stress functions: stress_HARA_RM_w(), stress_RM_w(), stress_VaR_ES(), stress_VaR(), stress_mean_sd_w(), stress_mean_sd(), stress_mean_w(), stress_mean(), stress_moment(), stress_prob(), stress_user(), stress_wass(), stress()

## Not run: 
set.seed(0)
x <- as.data.frame(cbind(
  "normal" = rnorm(1000),
  "gamma" = rgamma(1000, shape = 2)))
res1 <- stress_wass(type = "RM mean sd", x = x,
  alpha = 0.9, q_ratio = 1.05, new_means=1, new_sd=0.9)
  summary(res1)

## calling stress_RM_w directly
## stressing "gamma"
res2 <- stress_RM_mean_sd_w(x = x, alpha = 0.9,
  q_ratio = 1.05, new_means=2.2, new_sd=1.5, k = 2)
summary(res2)

## End(Not run)