now with endogeneity

merton_duncan.r

library(matlib)

gamma <- 2
rho11 <- 1.15
rho22 <- 0.05
mu1 <- 0.3
r <- 0.05
delta <- 0.05

x <- rnorm(1000000)
y <- rnorm(1000000) + 0.5*(mu1*(200/110000)/0.022)*x 
mu2 <- 0.1 + 0.2*(mu1*(200/110000)/0.022)
rho21 <- sqrt(cov(x,y))
rho12 <- rho21
rho21
rho11 * rho22 - rho21^2

omega <- matrix(data = c(rho11, rho21, rho12, rho22), nrow = 2, ncol = 2)
nretn <- c(mu1 - r, mu2 -r)
as.numeric((delta/gamma) - (1-gamma)*((r/gamma) + ((nretn %*% inv(omega) %*% nretn)/(2*(gamma^2))))) #consumption
c((1/gamma) * inv(matrix(data = c(rho11, rho21, rho12, rho22), nrow = 2, ncol = 2)) %*% c(mu1 - r, mu2 -r), 1-sum((1/gamma) * inv(matrix(data = c(rho11, rho21, rho12, rho22), nrow = 2, ncol = 2)) %*% c(mu1 - r, mu2 -r))) #allocation, AI vs non-AI stock