FastExpected: Fast expected value function

In rcss: Convex Switching Systems

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.

Author(s)

Jeremy Yee

Examples

## 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)

rcss documentation built on May 1, 2019, 10:13 p.m.