FiniteAddDual: Finite distribution case additive duals

In rcss: Convex Switching Systems

Description

Additive duals for finite distribution case. No nested simulation.

Usage

FiniteAddDual(path, disturb, grid, value, expected, build = "fast", k = 1)

Arguments

path	3-D array representing sample paths. Entry [i,,j] represents the state at time j for sample path i.
disturb	4-D array containing the disturbances used to generate the paths. Matrix [,,i,t] represents the disturbance at time t 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.
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 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.
build	string indicating which build method used to obtain expected value functions: "fast", "accelerated", and "slow".
k	Number of nearest neighbours used for "accelerated" build.

Value

3-D array where entry [i,p,t] represents the martingale increment at time t for position p on sample path i.

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)
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 <- sample(quantile, 100 * 50 / 2, TRUE)
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$expected)
## Scrap function
ScrapFunc <- function(state) {
    output <- array(data = 0, dim = c(nrow(state), 2))
    output[,2] <- exp(-0.06 * 0.02 * 50) * pmax(40 - state[,2], 0)
    return(output)
}
## Additive duals
mart <- FiniteAddDual(path, path_disturb, grid, bellman$value, bellman$expected, "fast")

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