Description Usage Arguments Value Author(s) Examples
Policy precribed to provided sample paths using nearest neighbours
1 | FastPathPolicy(path, grid, control, Reward, expected)
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path |
3-D array representing sample paths. Entry [i,,j] represents the state at time j for sample path i. |
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. |
control |
Array representing the transition probabilities of the controlled Markov chain. Two possible inputs:
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Reward |
User supplied function to represent the reward function. The function should take in the following arguments, in this order:
The function should output the following:
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expected |
4-D array representing the tangent approximation of the expected value function, where the intercept [i,1,p,t] and slope [i,-1,p,t] describes a tangent at grid point i for position p at time t. |
3-D array representing the prescribed policy for the sample paths. Entry [i,p,t] gives the prescribed action at time t for position p on sample path t.
Jeremy Yee
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | ## 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)
suppressWarnings(RNGversion("3.5.0"))
set.seed(12345)
start <- c(1, 36) ## starting state
path_disturb <- array(0, dim = c(2, 2, 100, 50))
path_disturb[1, 1,,] <- 1
rand1 <- rnorm(100 * 50 / 2)
rand1 <- as.vector(rbind(rand1, -rand1)) ## anti-thetic disturbances
path_disturb[2, 2,,] <- exp((0.06 - 0.5 * 0.2^2) * 0.02 + 0.2 * sqrt(0.02) * rand1)
path <- PathDisturb(start, path_disturb)
## Reward function
RewardFunc <- function(state, time) {
output <- array(data = 0, dim = c(nrow(state), 2, 2))
output[,2, 2] <- exp(-0.06 * 0.02 * (time - 1)) * pmax(40 - state[,2], 0)
return(output)
}
policy <- FastPathPolicy(path, grid, control, RewardFunc, bellman$expected)
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