CARA {GE}

Constant Absolute Risk Aversion (CARA) Utility Function

Description

Compute the value and the certainty equivalent of the CARA utility function, i.e. -exp(-gamma*x). In general equilibrium analysis, the CARA utility function has an interval scale like temperature.

Usage

CARA(x, gamma, prob = rep(1/length(x), length(x)))

Arguments

x

a payoff k-vector.

gamma

the Arrow-Pratt measure of absolute risk aversion.

prob

a probability k-vector. By default, the states are assumed to occur with equal probability.

Value

A list containing the following components:

• u: the utility level.

• CE: the certainty equivalent.

Examples

mu <- 5 # mu <- 8
a <- 1
x <- c(mu - a, mu + a)
gamma <- 0.8
mu - CARA(x, gamma)$CE

####
gamma <- 0.8
mu <- 2
sigma <- 2
x <- seq(mu - 5 * sigma, mu + 5 * sigma, length.out = 10000)
# two CE calculation methods for random variables of normal distribution
CARA(x, gamma, dnorm(x, mean = mu, sd = sigma))
mu - gamma * sigma^2 / 2