rcss (version 1.8)

FastExpected: Fast expected value function

Description

Approximate the expected value function using conditional expectaion matrices.

Usage

FastExpected(grid, value, disturb, weight, r_index, smooth = 1)

Arguments

grid

Matrix representing the grid. The i-th row corresponds to i-th point of the grid. The j-th column captures the dimensions. The first column must equal to 1.

value

Matrix representing the tangent approximation of the future value function, where the intercept [i,1] and slope [i,-1] describes a tangent at grid point i.

disturb

3-D array containing the disturbance matrices. Matrix [,,i] specifies the i-th disturbance matrix.

weight

Array containing the probability weights of the disturbance matrices.

r_index

Matrix representing the positions of random entries in the disturbance matrix, where entry [i,1] is the row number and [i,2] gives the column number of the i-th random entry.

smooth

The number of nearest neighbours used to smooth the expected value functions during the Bellman recursion.

Value

Matrix representing the tangent approximation of the expected value function. Same format as the value input.

Examples

# NOT RUN {
## Bermuda put option
grid <- as.matrix(cbind(rep(1, 81), c(seq(20, 60, length = 81))))
disturb <- array(0, dim = c(2, 2, 100))
disturb[1, 1,] <- 1
quantile <- qnorm(seq(0, 1, length = (100 + 2))[c(-1, -(100 + 2))])
disturb[2, 2,] <- exp((0.06 -0.5 * 0.2^2) * 0.02 + 0.2 * sqrt(0.02) * quantile)
weight <- rep(1 / 100, 100)
control <- matrix(c(c(1, 2),c(1, 1)), nrow = 2)
reward <- array(data = 0, dim = c(81, 2, 2, 2, 50))
in_money <- grid[, 2] <= 40
reward[in_money, 1, 2, 2,] <- 40
reward[in_money, 2, 2, 2,] <- -1
for (tt in 1:50){
  reward[,,2,2,tt] <- exp(-0.06 * 0.02 * (tt - 1)) * reward[,,2,2,tt] 
}
scrap <- array(data = 0, dim = c(81, 2, 2))
scrap[in_money, 1, 2] <- 40
scrap[in_money, 2, 2] <- -1
scrap[,,2] <- exp(-0.06 * 0.02 * 50) * scrap[,,2]
r_index <- matrix(c(2, 2), ncol = 2)
bellman <- FastBellman(grid, reward, scrap, control, disturb, weight, r_index)
expected <- FastExpected(grid, bellman$value[,,2,2], disturb, weight, r_index)
# }