/* Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved. File : portfolio_3_impact.java Purpose : Implements a basic portfolio optimization model with transaction costs of the form x^(3/2). */ package com.mosek.example; import mosek.solsta; import mosek.Exception; public class portfolio_3_impact { public static void main (String[] args) { // Since the value infinity is never used, we define // 'infinity' symbolic purposes only double infinity = 0; int n = 8; double[] mu = {0.07197, 0.15518, 0.17535, 0.08981, 0.42896, 0.39292, 0.32171, 0.18379}; double[][] GT = { {0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638}, {0. , 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506}, {0. , 0. , 0.19914, 0.05867, 0.06453, 0.07367, 0.06468, 0.01914}, {0. , 0. , 0. , 0.20876, 0.04933, 0.03651, 0.09381, 0.07742}, {0. , 0. , 0. , 0. , 0.36096, 0.12574, 0.10157, 0.0571 }, {0. , 0. , 0. , 0. , 0. , 0.21552, 0.05663, 0.06187}, {0. , 0. , 0. , 0. , 0. , 0. , 0.22514, 0.03327}, {0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.2202 } }; int k = GT.length; double[] x0 = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}; double w = 1.0; double gamma = 0.36; double totalBudget; double[] m = new double[n]; for (int i = 0; i < n; ++i) { m[i] = 0.01; } // Offset of variables into the API variable. int numvar = 3 * n; int voff_x = 0; int voff_c = n; int voff_z = 2 * n; // Offset of constraints. int numcon = 2 * n + 1; int coff_bud = 0; int coff_abs1 = 1; int coff_abs2 = 1 + n; try (mosek.Task task = new mosek.Task() ) { // Directs the log task stream to the user specified // method task_msg_obj.stream task.set_Stream( mosek.streamtype.log, new mosek.Stream() { public void stream(String msg) { System.out.print(msg); }}); // Variables (vector of x, c, z) task.appendvars(numvar); for (int j = 0; j < n; ++j) { /* Optionally we can give the variables names */ task.putvarname(voff_x + j, "x[" + (j + 1) + "]"); task.putvarname(voff_c + j, "c[" + (j + 1) + "]"); task.putvarname(voff_z + j, "z[" + (j + 1) + "]"); /* Apply variable bounds (x >= 0, c and z free) */ task.putvarbound(voff_x + j, mosek.boundkey.lo, 0.0, infinity); task.putvarbound(voff_c + j, mosek.boundkey.fr, -infinity, infinity); task.putvarbound(voff_z + j, mosek.boundkey.fr, -infinity, infinity); } // Linear constraints // - Total budget task.appendcons(1); task.putconname(coff_bud, "budget"); for (int j = 0; j < n; ++j) { /* Coefficients in the first row of A */ task.putaij(coff_bud, voff_x + j, 1.0); task.putaij(coff_bud, voff_c + j, m[j]); } totalBudget = w; for (int i = 0; i < n; ++i) { totalBudget += x0[i]; } task.putconbound(coff_bud, mosek.boundkey.fx, totalBudget, totalBudget); // - Absolute value task.appendcons(2 * n); for (int i = 0; i < n; ++i) { task.putconname(coff_abs1 + i, "zabs1[" + (1 + i) + "]"); task.putaij(coff_abs1 + i, voff_x + i, -1.0); task.putaij(coff_abs1 + i, voff_z + i, 1.0); task.putconbound(coff_abs1 + i, mosek.boundkey.lo, -x0[i], infinity); task.putconname(coff_abs2 + i, "zabs2[" + (1 + i) + "]"); task.putaij(coff_abs2 + i, voff_x + i, 1.0); task.putaij(coff_abs2 + i, voff_z + i, 1.0); task.putconbound(coff_abs2 + i, mosek.boundkey.lo, x0[i], infinity); } // ACCs int aoff_q = 0; int aoff_pow = k + 1; // - (gamma, GTx) in Q(k+1) // The part of F and g for variable x: // [0, 0, 0] [gamma] // F = [GT, 0, 0], g = [0 ] task.appendafes(k + 1); task.putafeg(aoff_q, gamma); int[] vslice_x = new int[n]; for (int i = 0; i < n; ++i) { vslice_x[i] = voff_x + i; } for (int i = 0; i < k; ++i) { task.putafefrow(aoff_q + i + 1, vslice_x, GT[i]); } long qdom = task.appendquadraticconedomain(k + 1); task.appendaccseq(qdom, aoff_q, null); task.putaccname(aoff_q, "risk"); // - (c_j, 1, z_j) in P3(2/3, 1/3) // The part of F and g for variables [c, z]: // [0, I, 0] [0] // F = [0, 0, I], g = [0] // [0, 0, 0] [1] task.appendafes(2 * n + 1); for (int i = 0; i < n; ++i) { task.putafefentry(aoff_pow + i, voff_c + i, 1.0); task.putafefentry(aoff_pow + n + i, voff_z + i, 1.0); } task.putafeg(aoff_pow + 2 * n, 1.0); // We use one row from F and g for both c_j and z_j, and the last row of F and g for the constant 1. // NOTE: Here we reuse the last AFE and the power cone n times, but we store them only once. double[] exponents = {2, 1}; long powdom = task.appendprimalpowerconedomain(3, exponents); long[] flat_afe_list = new long[3 * n]; long[] dom_list = new long[n]; for (int i = 0; i < n; ++i) { flat_afe_list[3 * i + 0] = aoff_pow + i; flat_afe_list[3 * i + 1] = aoff_pow + 2 * n; flat_afe_list[3 * i + 2] = aoff_pow + n + i; dom_list[i] = powdom; } task.appendaccs(dom_list, flat_afe_list, null); for (int i = 0; i < n; ++i) { task.putaccname(i + 1, "market_impact[" + i + "]"); } // Objective: maximize expected return mu^T x for (int j = 0; j < n; ++j) { task.putcj(voff_x + j, mu[j]); } task.putobjsense(mosek.objsense.maximize); /* Solve the problem */ try { //Turn all log output off. //task.putintparam(mosek.iparam.log,0); task.writedata("dump.ptf"); task.optimize(); task.solutionsummary(mosek.streamtype.log); // Check if the interior point solution is an optimal point solsta solsta = task.getsolsta(mosek.soltype.itr); if (solsta != mosek.solsta.optimal) { // See https://docs.mosek.com/latest/javaapi/accessing-solution.html about handling solution statuses. throw new Exception(6010, String.format("Unexpected solution status: %s", solsta)); } double expret = 0.0, stddev = 0.0; double[] xx = task.getxx(mosek.soltype.itr); for (int j = 0; j < n; ++j) expret += mu[j] * xx[j + voff_x]; System.out.printf("Expected return %e for gamma %e\n\n", expret, gamma); } catch (mosek.Warning mw) { System.out.println (" Mosek warning:"); System.out.println (mw.toString ()); } } catch ( mosek.Exception e) { System.out.println ("An error/warning was encountered"); System.out.println (e.toString ()); throw e; } } }