Models in Neglectedness

field_size_1 = 3

rho = 0.1 to 0.8

neglectedness_1 = field_size_1^-rho
r5 = quantile(rho, 0.05)
r95 = quantile(rho, 0.95)
n50 = quantile(neglectedness_1, 0.5) // n50 is neglectedness under median Rho assumption

approx_1 = n50^(rho/(r5*r95)^0.5)

/*
Describe your code here
*/

// Sample two field sizes from a distribution
a = truncate(1 to 1000, .1, 10000) // Lognormal, with extreme values cut off
b = truncate(1 to 1000, .1, 10000)

// Ratio between size of two randomly chosen fields
ratio = max(a/b, b/a)

/*
Describe your code here
*/

rho1 = uniform(0,1)
rho2 = normal(0.5, 0.25)
rho3 = 2*beta(1,3)

rho = mx(rho1,rho2,rho3,[1,1,1]) // unweighted mixture of the above

/*
Exploring Isoelastic Utility Functions (IUF) under semi-efficient market conditions
*/

// What if we are uncertain about Rho and model it as lognormally distributed?
// This could be justifiable if we think that 100% efficient markets are impossible to achieve, and log(rho) is normally distributed

rho_lognormal = 0.1 to 1

// vmf is value of marginal funding. It is the gradient of the IUF, x^-rho.

/*
Exploring Isoelastic Utility Functions (IUF) under semi-efficient market conditions
*/

// CURRENTLY THIS IS MOSTLY A COPY OF THE EFFICIENT MARKET MODEL

// What if we are uncertain about Rho and model it as lognormally distributed?
// This could be justifiable if we think that 100% efficient markets are impossible to achieve, and log(rho) is normally distributed

rho_lognormal = 1 - (0.1 to 1)

/*
Describe your code here
*/

// For Isoelastic Utility Functions (IUFs), 'compounding' fields have increasing returns, so rho < 0.
// Diminishing returns means rho > 1

// We want to know whether modelling rho as a distribution is comparable (in terms of central values) to
// using a discounted point-estimate rho instead.