AMSD {GE}

Additive-Mean-Variance Utility Function and Additive-Mean-Standard-Deviation Utility Function

Description

Compute the utility function mean(x) - (gamma * sd.p(x))^theta / theta or weighted.mean(x, wt) - (gamma * sd.p(x, wt))^theta / theta.

Usage

AMSD(x, gamma = 1, wt = NULL, theta = 1)

AMV(x, gamma = 1, wt = NULL)

Arguments

x

a numeric n-vector.

gamma

a non-negative scalar representing the risk aversion coefficient with a default value of 1.

wt

a numeric n-vector of weights (or probability). If wt is NULL, all elements of x are given the same weight.

theta

a non-negative scalar with a default value of 1.

Value

A scalar indicating the utility level.

Functions

• AMSD: Computes the utility function mean(x) - (gamma * sd.p(x))^theta / theta or weighted.mean(x, wt) - (gamma * sd.p(x, wt))^theta / theta. When theta == 2, it is the additive mean-variance utility function (i.e. the function AMV). When theta == 1 (the default value), it is the additive mean and standard deviation utility function.

• AMV: Compute the additive mean-variance utility function mean(x) - 0.5 * gamma * var.p(x) or weighted.mean(x, wt) - 0.5 * gamma * var.p(x, wt).

References

Nakamura, Yutaka (2015). Mean-Variance Utility. Journal of Economic Theory, 160: 536-556.

Examples

AMSD(1:2, gamma = 0.05)
AMSD(1:2, gamma = 1, theta = 2)

marginal_utility(
  c(1, 1.001),
  c(0, 1), function(x) AMSD(x, gamma = 0.5)
)
marginal_utility(
  c(1.001, 1),
  c(0, 1), function(x) AMSD(x, gamma = 0.5)
)