GE (version 0.2.5)

AMSDP: Additive-Mean-Standard-Deviation Portfolio Utility Function

Description

Compute the utility function x %*% mp - 0.5 * gamma * (t(x) %*% Cov %*% x)^(0.5 * theta) for a portfolio x.

Usage

AMSDP(x, mp, Cov, gamma = 1, theta = 1)

Arguments

x

a numeric n-vector representing a portfolio.

mp

a numeric n-vector representing the mean payoff of each of the n securities.

Cov

the n-by-n covariance matrix of the payoff vectors of n securities.

gamma

the risk aversion coefficient.

theta

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

References

Danthine, J. P., Donaldson, J. (2005, ISBN: 9780123693808) Intermediate Financial Theory. Elsevier Academic Press.

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

Sharpe, William F (2008, ISBN: 9780691138503) Investors and Markets: Portfolio Choices, Asset Prices, and Investment Advice. Princeton University Press.

Xu Gao (2018, ISBN: 9787300258232) Twenty-five Lectures on Financial Economics. Beijing: China Renmin University Press. (In Chinese)

See Also

AMSD

Examples

# NOT RUN {
#### an example of security pricing with two heterogeneous agents who have
## different beliefs and predict different payoff vectors.

## the predicted payoff vectors of agent 1 on the two securities.
secy1.1 <- c(1, 2, 2, 0)
secy2.1 <- c(2, 2, 0, 2)

## the predicted payoff vectors of agent 2 on the two securities.
secy1.2 <- c(1, 0, 2, 0)
secy2.2 <- c(2, 1, 0, 2)

secy3 <- c(1, 1, 1, 1)

## the unit security payoff matrix of agent 1.
USP1 <- cbind(secy1.1, secy2.1, secy3)

## the unit security payoff matrix of agent 2.
USP2 <- cbind(secy1.2, secy2.2, secy3)

mp1 <- colMeans(USP1)
Cov1 <- cov.wt(USP1, method = "ML")$cov

mp2 <- colMeans(USP2)
Cov2 <- cov.wt(USP2, method = "ML")$cov

## the utility function of agent 1.
uf1 <- function(x) AMSDP(x, mp1, Cov1, gamma = 2)

## the utility function of agent 2.
uf2 <- function(x) AMSDP(x, mp2, Cov2, gamma = 2)


ge <- sdm2(
  A = function(state) {
    Portfolio <- state$last.A %*% dg(state$last.z)

    VMU <- marginal_utility(Portfolio, diag(3), list(uf1, uf2), state$p)

    Ratio <- sweep(VMU, 2, colMeans(VMU), "/")

    A <- state$last.A * ratio_adjust(Ratio, coef = 0.15, method = "linear")
    prop.table(A, 2)
  },
  B = matrix(0, 3, 2),
  S0Exg = matrix(c(
    1, 5,
    2, 5,
    3, 5
  ), 3, 2, TRUE),
  names.commodity = c("secy1", "secy2", "secy3"),
  names.agent = c("agt1", "agt2"),
  numeraire = "secy3",
  maxIteration = 1,
  numberOfPeriods = 1000,
  ts = TRUE
)

ge$p
ge$D
marginal_utility(ge$D[, 1], diag(3), uf1) / ge$p
marginal_utility(ge$D[, 2], diag(3), uf2) / ge$p
# }