AMSD | R Documentation |
Compute the utility function mean(x) - (gamma * sd.p(x))^theta / theta or weighted.mean(x, wt) - (gamma * sd.p(x, wt))^theta / theta.
AMSD(x, gamma = 1, wt = NULL, theta = 1)
AMV(x, gamma = 1, wt = NULL)
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. |
A scalar indicating the utility level.
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).
Nakamura, Yutaka (2015). Mean-Variance Utility. Journal of Economic Theory, 160: 536-556.
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)
)
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