gemAssetExchange_MatthewEffect_2_2 {GE}

An Example Illustrating the Matthew Effect of Asset Exchange

Description

This is an example that illustrates the Matthew effect of asset exchange, wherein the wealth gap between two traders widens after the exchange process. Initially, these traders had a relatively small wealth (i.e. expected average payoff) gap. However, the exchange leads to an expansion of the wealth gap. This outcome can be attributed to the fact that a trader's risk aversion coefficient is affected by his level of wealth. When traders have less wealth their risk aversion coefficient is higher. Consequently, a trader with less wealth tends to acquire more low-risk, low-average-payoff assets through trading. As a result, the expected average payoff of a trader with less wealth may decrease after the exchange. Conversely, a trader with more wealth may hold more high-risk, high-average-payoff assets after trading.

Usage

gemAssetExchange_MatthewEffect_2_2(...)

Arguments

...

arguments to be passed to the function sdm2.

See Also

gemAssetPricing_PUF.

Examples

#### Matthew effect
asset1 <- c(40, 200)
asset2 <- c(100, 100)

# unit asset payoff matrix.
UAP <- cbind(asset1, asset2)

S <- matrix(c(
  0.49, 0.51,
  0.49, 0.51
), 2, 2, TRUE)

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

    Payoff <- UAP %*% Portfolio
    payoff.average <- colMeans(Payoff)

    # the risk aversion coefficients.
    rac <- ifelse(payoff.average > mean(UAP) * 1.02, 0.5, 1)
    rac <- ifelse(payoff.average < mean(UAP) / 1.02, 2, rac)

    uf1 <- function(portfolio) {
      payoff <- UAP %*% portfolio
      CES(alpha = 1, beta = c(0.5, 0.5), x = payoff, es = 1 / rac[1])
    }

    uf2 <- function(portfolio) {
      payoff <- UAP %*% portfolio
      CES(alpha = 1, beta = c(0.5, 0.5), x = payoff, es = 1 / rac[2])
    }

    VMU <- marginal_utility(Portfolio, diag(2), list(uf1, uf2), state$p)
    VMU <- pmax(VMU, 1e-10)

    Ratio <- sweep(VMU, 2, colMeans(VMU), "/")
    A <- state$last.A * ratio_adjust(Ratio, coef = 0.1, method = "linear")

    prop.table(A, 2)
  },
  B = matrix(0, 2, 2),
  S0Exg = S,
  names.commodity = c("asset1", "asset2"),
  numeraire = 2,
  maxIteration = 1,
  numberOfPeriods = 1000,
  policy = makePolicyMeanValue(50),
  ts = TRUE
)

matplot(ge$ts.p, type = "l")
ge$p
ge$z
ge$D

(Payoff.S <- UAP %*% S)
colMeans(Payoff.S)

(Payoff.D <- UAP %*% ge$D)
colMeans(Payoff.D)

## Calculate the equilibrium under the fixed risk aversion coefficients.
rac <- c(2, 0.5)

uf <- list()
uf[[1]] <- function(portfolio) {
  payoff <- UAP %*% portfolio
  CES(alpha = 1, beta = c(0.5, 0.5), x = payoff, es = 1 / rac[1])
}

uf[[2]] <- function(portfolio) {
  payoff <- UAP %*% portfolio
  CES(alpha = 1, beta = c(0.5, 0.5), x = payoff, es = 1 / rac[2])
}

ge <- gemAssetPricing_PUF(
  S = S,
  uf = uf,
  policy = makePolicyMeanValue(50)
)

ge$p
addmargins(ge$D, 2)
addmargins(ge$S, 2)
ge$VMU

(Payoff <- UAP %*% ge$D)
colMeans(Payoff)