stress_mean_w {SWIM}

Stressing Mean

Description

Provides weights on simulated scenarios from a baseline stochastic model, such that a stressed model component (random variable) fulfils a constraint on its mean. Scenario weights are selected by constrained minimisation of the Wasserstein distance to the baseline model.

Usage

stress_mean_w(
  x,
  new_means,
  k = 1,
  h = 1,
  names = NULL,
  log = FALSE,
  method = "Nelder-Mead",
  ...
)

Arguments

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.

new_means

Numeric, the stressed mean.

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).

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.

Value

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 = "mean";

• specs, a list, each component corresponds to a different stress and contains k and new_means.

See SWIM for details.

Author(s)

Zhuomin Mao

References

Pesenti SM, Millossovich P, Tsanakas A (2019). “Reverse sensitivity testing: What does it take to break the model?” European Journal of Operational Research, 274(2), 654–670.

Pesenti S BAMPTA (2020). “Scenario Weights for Importance Measurement (SWIM) - An R package for sensitivity analysis.” Annals of Actuarial Science 15.2 (2021): 458-483. Available at SSRN: https://www.ssrn.com/abstract=3515274.

Pesenti SM (2021). “Reverse Sensitivity Analysis for Risk Modelling.” Available at SSRN 3878879.

See Also

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

Examples

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

## calling stress_RM_w directly
## stressing "gamma"
res2 <- stress_mean_w(x = x, 
  new_means=2.2, k = 2)
summary(res2)

## End(Not run)