Description Usage Arguments Value Author(s) Examples
Approximate the value functions using k nearest neighbours.
1 | AcceleratedBellman(grid, reward, scrap, control, disturb, weight, k = 1)
|
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. |
reward |
5-D array representing the tangent approximation of the reward. Entry [i,,a,p,t] captures the tangent at grid point i for action a taken in position p at time t. The intercept is given by [i,1,a,p,t] and slope by [i,-1,a,p,t]. |
scrap |
3-D array representing the tangent approximation of the scrap. Entry [i,,p] captures the tangent at grid point i for position p. The intercept is given by [i,1,p] and slope by [i,-1,p]. |
control |
Array representing the transition probabilities of the controlled Markov chain. Two possible inputs:
|
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. |
k |
Number of nearest neighbours used for each grid point. |
value |
4-D array tangent approximation of the value function, where the intercept [i,1,p,t] and slope [i,-1,p,t] describes a tangent of the value function at grid point i for position p at time t. |
expected |
4-D array representing the expected value functions. |
Jeremy Yee
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ## 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 <- AcceleratedBellman(grid, reward, scrap, control, disturb, weight)
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