Description

Additive duals for finite distribution case. No nested simulation.

Usage

 `1` ```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.

Jeremy Yee

Examples

 ``` 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 38 39 40 41 42 43 44 45``` ```## 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.