rcss (version 1.1)

ExpectedAccelerated: Expected Value Function Using K Nearest Neighbours

Description

Approximate the expected value function using k nearest neighbours.

Usage

ExpectedAccelerated(grid, value, disturb, weight, k, Neighbour)

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.

k

The number of nearest neighbours for each grid point. Must be greater than 1.

Neighbour

Optional function to find the nearest neighbours. If not provided, the Neighbour function from the rflann package is used instead.

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 <- BellmanAccelerated(grid, reward, control, disturb, weight, 2)
expected <- ExpectedAccelerated(grid, bellman$value[,,2,2], disturb, weight, 2)