Expected: Expected value function

In rcss: Convex Switching Systems

Description

Approximate the expected value function by comparing all tangents.

Usage

Expected(grid, value, disturb, weight)

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.

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]
bellman <- Bellman(grid, reward, scrap, control, disturb, weight)
expected <- Expected(grid, bellman$value[,,2,2], disturb, weight)

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