# file Reed.R
# author Carl Boettiger, <cboettig@gmail.com>
# date 2011-11-02
# license BSD
# modified from Reed_SDP.m, by Michael Bode.
#
# Implements a numerical version of the SDP described in:
# Reed, W.J., 1979. Optimal Escapement Levels in Stochastic
# and Deterministic Harvesting Models. Journal of Environmental
# Economics and Management. 6: 350-363.
#
# Fish population dynamics:
# X_{t+1} = Z_n f(X_n)
require(pdgControl)
require(reshape2)
require(ggplot2)
## consider defaults for these
# Define all parameters
delta <- 0.05 # economic discounting rate
OptTime <- 50 # stopping time
gridsize <- 10 # gridsize (discretized population)
sigma_g <- 0.2 # Noise in population growth
# load noise distributions
z_g <- function() rlnorm(1, 0, sigma_g) # mean 1
### Chose the state equation / population dynamics function
f <- BevHolt # Select the state equation
pars <- c(1.5, 0.05) # parameters for the state equation
xT <- 0 # boundary conditions
x0 <- 10
profit <- profit_harvest()
# Set up the discrete grids
x_grid <- seq(0, 12, length = gridsize) # population size
h_grid <- x_grid # vector of havest levels, use same resolution as for stock
SDP_Mat <- determine_SDP_matrix(f, pars, x_grid, h_grid, sigma_g )
opt <- find_dp_optim(SDP_Mat, x_grid, h_grid, OptTime, xT, profit, delta)
ForwardSimulate(f,pars,x_grid,h_grid,x0, opt$D, z_g)
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