Market Impact Optimal Execution Part 1.txt

reset;


param N integer;
param lambda;
param X integer;
param eta;
param sigma;


var x{i in 0..N};


minimize execution_cost:
eta*(X-x[1])**2 + 2*eta*(sum{k in 2..N} (x[k-1]-x[k])**2)+ lambda*sigma**2*sum{k in 1..N} x[k]**2;

subject to total: sum{k in 1..N} x[k] = X;


data;
param N := 5;
param lambda := 0.006;
param X := 1000000;
param eta := .000001;
param sigma := 0.01;


option solver gurobi;
solve;


printf {k in 1..2}: "%10.7f ", x[k];
printf {k in 3..N}: "%10.7f ", x[k];