rcss (version 1.1)

Expected: Expected Value Function

Description

Approximate the expected value functions.

Usage

Expected(grid, value, disturb, weight)

Arguments

grid

Matrix representing the grid, whose i-th row matrix [i,] corresponds to i-th point of the grid. The matrix [i,1] equals to 1 while the vector [i,-1] represents the system state.

value

Matrix representing the subgradient envelope of the future value function, where the intercept [i,1] and slope matrix [i,-1] describes a subgradient at grid point i.

disturb

3-dimensional 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 subgradient envelope of the expected value function. Same format as the value input.

Examples

## Bermuda put option
grid <- as.matrix(cbind(rep(1, 91), c(seq(10, 100, length = 91))))
disturb <- array(0, dim = c(2, 2, 10))
disturb[1, 1,] <- 1
disturb[2, 2,] <- exp((0.06 - 0.5 * 0.2^2) * 0.02 + 0.2 * sqrt(0.02) * rnorm(10))
weight <- rep(1 / 10, 10)
control <- matrix(c(c(1, 2),c(1, 1)), nrow = 2)
reward <- array(data = 0, dim = c(91, 2, 2, 2, 51))
reward[grid[, 2] <= 40, 1, 2, 2,] <- 40
reward[grid[, 2] <= 40, 2, 2, 2,] <- -1
bellman <- Bellman(grid, reward, control, disturb, weight)
expected <- Expected(grid, bellman$value[,,2,2], disturb, weight)