public static double Run(string type, double[] prms, double[] gpath, int fxTD, double rf0, long n, int nbuckets, int prec, int plproc, double mxgrd, double stdpnr, long npnr, double[] grdnt, double alpha, int nitrs = 0)
{
double maxpnr = stdpnr;
double iter = 1.00;
int[] prtls = { -1, -1, -1, -1 };
long maxn = npnr;
int cont = 1;
int fstimpr = 0;
int iindx = 0;
int tryup = 0;
int origindx = 0;
NormalDistribution normdist = new NormalDistribution(0.00, 1.00);
// Get initial glidepath provided, assign to both original GP array and prior GP array.
var prevGP = new double[fxTD];
var origGP = new double[fxTD];
for (int y = 0; y < fxTD; ++y)
{
origGP[y] = prevGP[y] = gpath[y];
}
// Define the step size for climbing. The step size depends on the largest gradient element and grows exponentially.
// This is a heuristic that has worked well and can be modified if desired. Better step sizes can reduce runtimes.
for (int i = 1; i <= 10; ++i)
{
if (mxgrd >= 1.00 / (10.00 * Math.Pow(10.00, i)) && mxgrd < 1.00 / (10.00 * Math.Pow(10.00, i - 1)))
{
iindx = i;
iter = Math.Pow(Math.Exp(Math.Log(5.00) / 4.00), iindx);
}
}
// Output details for the current iteration.
Trace.WriteLine(new String('=', 70));
Trace.WriteLine($"Iteration step size = {iter:F10}");
Trace.Write("Trying to improve on success probability = ");
Trace.WriteLine(stdpnr);
Trace.WriteLine(new String('=', 70));
// Climb in the direction of the gradient.
for (int t = 0; cont == 1 || fstimpr == 0; ++t) // Iterate until no more progress is made
{
if (cont == 0 && fstimpr == 0) // If no progress is made reduce step size and try again.
{
// Set the original index value when entering this problematic scenario.
if (origindx == 0)
{
origindx = iindx;
}
// Adjust glidepath back one iteration since it failed to improve the probability.
for (int y = 0; y < fxTD; ++y)
{
gpath[y] = prevGP[y]; // Reverse final update, since no progress was made.
}
if (iindx != 0)
{
}
Trace.WriteLine("");
Trace.Write("No Progress Made: Iteration step size changed from ");
Trace.Write(iter);
if (iindx == 0)
{
Trace.WriteLine(" to 0.00. (No additional climbing attempts will be made.)");
Trace.WriteLine("");
Trace.WriteLine("ERROR: No progress can be made, the procedure is stuck. (Step size has been reduced to 0.)");
Trace.WriteLine(" You may be operating along the boundary where the process is not well defined or your");
Trace.WriteLine(" estimation/approximation precision level is not adequate for your epsilon level.");
Trace.WriteLine("");
Trace.WriteLine("");
Trace.Write("Current Glide-Path: ");
WrtAry.Run(maxpnr, gpath, "GP", fxTD);
Trace.WriteLine("");
Trace.WriteLine("EXITING...Climb()...");
Console.Read();
Environment.Exit(1);
}
else if (iindx == 1 && tryup == 5)
{
iindx = iindx - 1;
iter = iter / 2.00;
}
else if (iindx > 1 && tryup == 5)
{
if (iindx == origindx + 5)
{
iindx = origindx - 1;
}
else
{
iindx = iindx - 1;
}
iter = Math.Pow(Math.Exp(Math.Log(5.00) / 4.00), iindx);
}
else if (iindx > 1 && tryup < 5)
{
iindx = iindx + 1;
iter = Math.Pow(Math.Exp(Math.Log(5.00) / 4.00), iindx);
tryup = tryup + 1;
}
Trace.Write(" to ");
Trace.Write(iter);
Trace.WriteLine(". (Attempting to climb again.)");
cont = 1;
}
for (int y = 0; y < fxTD; ++y) // Iterate over glide-path and update it
{
prevGP[y] = gpath[y]; // Reset the previous glide-path element
gpath[y] = gpath[y] + (iter) * grdnt[y]; // Update each individual glide-path element
if (gpath[y] < Funcs.mva(prms) + 0.0001)
{
gpath[y] = Funcs.mva(prms) + 0.0001; // Stay above MVA and consistent with ThrdPNRdyn() and ThrdPNRsim().
}
else if (gpath[y] > 1.00)
{
gpath[y] = 1.00; // Consistent with ThrdPNRdyn() and ThrdPNRsim().
}
}
double newpnr = GetPNR.Run(type, prms, gpath, fxTD, rf0, n, nbuckets, prec, prtls, plproc);
Trace.WriteLine("");
Trace.Write("Base Prob(NR) = ");
Trace.Write(maxpnr);
if (type == "sim")
{
Trace.Write(" (N=");
Trace.Write(maxn);
Trace.Write(")");
}
Trace.WriteLine("");
Trace.Write("New Prob(NR) = ");
Trace.Write(newpnr);
if (type == "sim")
{
Trace.Write($" (N={n})");
}
else if (newpnr > maxpnr)
{
Trace.Write(" (Better, CONTINUE climbing ...)");
}
else
{
Trace.Write(" (Worse, STOP climbing ...)");
}
Trace.WriteLine("");
// If using simulation, conduct a non-inferiority test of the new vs max base GP.
// =====> Continue to climb if the new GP is at least as good as the max base GP.
// Otherwise, compare new probability with old and climb while making progress.
if (type == "sim")
{
double cmbvar = maxpnr * (1.00 - maxpnr) / maxn + newpnr * (1.00 - newpnr) / n;
double ts = (newpnr - maxpnr) / Math.Sqrt(cmbvar);
double pval = normdist.DistributionFunction(ts);
Trace.Write("Test Statistic = ");
Trace.WriteLine(ts);
Trace.Write("P-Value = ");
Trace.Write(pval);
Trace.Write(" (Alpha=");
Trace.Write(alpha);
Trace.WriteLine(")");
if (pval > alpha)
{
fstimpr = 1;
Trace.WriteLine("=====> Accept Ho (non-inferiority), CONTINUE climbing ...");
}
else
{
cont = 0;
Trace.WriteLine("=====> Reject Ho (non-inferiority), STOP climbing ...");
}
// Update PNR and sample size for base GP.
if (newpnr > maxpnr)
{
maxpnr = newpnr;
maxn = n;
}
}
else if (type == "dp")
{
if (newpnr > maxpnr)
{
fstimpr = 1;
maxpnr = newpnr;
}
else
{
cont = 0;
}
}
// For lengthy climbing, display the current glidepath at 100 iteration intervals.
if ((t + 1) % 100 == 0)
{
Trace.WriteLine("");
Trace.Write("Current Glide-Path at Iteration: ");
Trace.Write(t + 1);
WrtAry.Run(newpnr, gpath, "GP", fxTD);
}
// Stop when maximum number of iterations has been reached, if specified.
//=========================================================================
if (nitrs > 0 && t + 1 == nitrs && cont == 1)
{
Trace.WriteLine("");
Trace.WriteLine($"Climbing limit reached at {nitrs} iterations.");
cont = 2;
}
}
// Adjust glidepath back one iteration since it failed to improve the probability.
// (This is only done when climbing failed to improve, not when limit is reached.)
if (cont != 2)
{
for (int y = 0; y < fxTD; ++y)
{
gpath[y] = prevGP[y];
}
}
if (type == "sim")
{
Trace.WriteLine("");
Trace.WriteLine("Resetting the probability (to remove any built-in upward sampling bias) ...");
maxpnr = ThrdPNRsim.Run(prms, gpath, fxTD, rf0, 2 * n, prtls, plproc);
}
// Return the max success probability.
return(maxpnr);
}
public static void Run(int pllproc)
{
double[] @params = new double[6];
double maxgrad = 0;
double stpthrsh = 0;
double maxeigen;
double mineigen;
double wr = 0;
double[] alpha = { 0.50, 1.00 };
double rfMax = 2.75;
int td = 0;
int[] prtls = { -1, -1, -1, -1 };
int iterint = 1;
long sn = (long)Math.Pow(10.0, 7);
int prec = (int)Math.Pow(10.0, 4);
string type = "";
string alg = "";
const string rootdir = Config.ConfigsRootDir;
// Read setup details from control file.
try
{
var getParams = File.ReadAllText(Path.Combine(rootdir, Config.ControlFile));
var s = getParams.Split(new[] { ' ', '\r', '\n' }, StringSplitOptions.RemoveEmptyEntries);
@params = s.Take(6).Select(i => double.Parse(i, CultureInfo.InvariantCulture)).ToArray();
td = int.Parse(s[6]);
wr = double.Parse(s[7]);
stpthrsh = double.Parse(s[8]);
alg = s[9];
type = s[10];
if (type.Equals("sim"))
{
sn = int.Parse(s[11]);
alpha[0] = double.Parse(s[12]);
alpha[1] = double.Parse(s[13]);
}
else if (type.Equals("dp"))
{
prec = int.Parse(s[11]);
rfMax = double.Parse(s[12]);
}
}
catch (Exception ex)
{
Trace.Write("ERROR: Could not read file: ");
Trace.WriteLine(Path.Combine(rootdir, Config.ControlFile) + $". {ex.Message}");
Trace.WriteLine("EXITING...main()...");
Console.Read();
Environment.Exit(1);
}
// Read initial glide-path from file.
var gp = new double[td];
var gpPath = Path.Combine(rootdir, Config.InitGladepathFile);
try
{
gp = File.ReadAllLines(gpPath).Select(double.Parse)
.Take(td).ToArray();
}
catch (Exception ex)
{
Trace.Write("ERROR: Could not read file: ");
Trace.WriteLine(gpPath + ". Error: " + ex.Message);
Trace.WriteLine("EXITING...main()...");
Console.Read();
Environment.Exit(1);
}
if (gp.Length != td)
{
Trace.Write("ERROR: File: ");
Trace.Write(gpPath);
Trace.Write(" needs ");
Trace.Write(td);
Trace.WriteLine(" initial asset allocations, but has fewer.");
Trace.WriteLine("EXITING...main()...");
Console.Read();
Environment.Exit(1);
}
// Display optimization algorithm.
Trace.Write(@"===> Optimization algorithm: ");
if (alg == "nr")
{
Trace.WriteLine(@"Newton's Method");
}
else if (alg == "ga")
{
Trace.WriteLine(@"Gradient Ascent");
}
// Display estimation method.
Trace.WriteLine("");
Trace.Write(@"===> Estimation method: ");
if (type == "sim")
{
Trace.WriteLine(@"Simulation");
}
else if (type == "dp")
{
Trace.WriteLine(@"Dynamic Program");
pllproc = 4 * pllproc;
}
// Declare variables that depend on data read from the control file for sizing.
double[,] hess;
double[] ngrdnt = new double[td];
EigenvalueDecomposition hevals;
var grad = new double[td];
// Take some steps (1 full iteration but no more than 50 steps) in the direction of steepest ascent. This can move us off
// the boundary region where computations may be unstable (infinite), especially when constructing the Hessian for Newton's method.
// Also, this initial stepping usually makes improvements very quickly before proceeding with the optimization routine.
double probnr = GetPNR.Run(type, @params, gp, td, wr, 4 * sn, (int)(rfMax * prec), prec, prtls, pllproc);
Trace.WriteLine("");
Trace.WriteLine("Initial Glide-Path (w/Success Probability):");
WrtAry.Run(probnr, gp, "GP", td);
for (int s = 1; s <= 2; ++s)
{
maxgrad = BldGrad.Run(type, @params, gp, td, wr, sn, (int)(rfMax * prec), prec, probnr, 4 * sn, alpha[1], pllproc, grad);
if (maxgrad <= stpthrsh)
{
Trace.Write("The glide-path supplied satisfies the EPSILON convergence criteria: ");
Trace.WriteLine($"{maxgrad:F15} vs. {stpthrsh:F15}");
s = s + 1;
}
else if (s != 2)
{
probnr = Climb.Run(type, @params, gp, td, wr, 2 * sn, (int)(rfMax * prec), prec, pllproc, maxgrad,
probnr, 4 * sn, grad, alpha[0], 50);
Trace.WriteLine("");
Trace.WriteLine("New (Post Initial Climb) Glide-Path (w/Success Probability):");
WrtAry.Run(probnr, gp, "GP", td);
}
else if (maxgrad <= stpthrsh)
{
Trace.Write("The glide-path supplied satisfies the EPSILON convergence criteria after intial climb without iterating: ");
Trace.WriteLine($"{maxgrad:F15} vs. {stpthrsh:F15}");
}
}
// Negate the gradient if using NR method.
if (alg == "nr")
{
for (int y = 0; y < td; ++y)
{
ngrdnt[y] = -1.00 * grad[y];
}
}
// If convergence is not achieved after initial climb then launch into full iteration mode.
while (maxgrad > stpthrsh)
{
Trace.WriteLine("");
Trace.WriteLine("=========================");
Trace.WriteLine($"Start Iteration #{iterint}");
Trace.WriteLine("=========================");
if (alg == "nr")
{
// Record the probability before iterating.
double strtpnr = probnr;
// Build the Hessian matrix for this glide-path and derive its eigenvalues. (Display the largest & smallest value.)
// This is required when method=nr. When either procedure ends with convergence we recompute the Hessian matrix to
// ensure we are at a local/global maximum (done below after convergence).
hess = DrvHess.Run(type, @params, gp, td, wr, sn, (int)(rfMax * prec), prec, pllproc, grad, probnr);
//hevals.compute(hess, false);
hevals = new EigenvalueDecomposition(hess);
var reals = hevals.RealEigenvalues;
maxeigen = reals.Max();
mineigen = reals.Min();
// Display the smallest/largest eigenvalues.
Trace.WriteLine("");
Trace.Write("Min Hessian eigenvalue for this iteration (>=0.00 --> convex region): ");
Trace.WriteLine(mineigen);
Trace.WriteLine("");
Trace.Write("Max Hessian eigenvalue for this iteration (<=0.00 --> concave region): ");
Trace.WriteLine(maxeigen);
// Update the glidepath and recompute the probability using the new glidepath.
//sol = hess.colPivHouseholderQr().solve(ngrdnt);
var qr = new QrDecomposition(hess);
var sol = qr.Solve(ngrdnt);
for (int y = 0; y < td; ++y)
{
gp[y] += sol[y];
}
probnr = GetPNR.Run(type, @params, gp, td, wr, 4 * sn, (int)(rfMax * prec), prec, prtls, pllproc);
// If success probability has worsened alert the user.
if (probnr < strtpnr)
{
Trace.WriteLine("");
Trace.WriteLine("NOTE: The success probability has worsened during the last iteration. This could happen for different reasons:");
Trace.WriteLine(" 1.) The difference in probabilities is beyond the system's ability to measure accurately (i.e., beyond 15 significant digits).");
Trace.WriteLine(" 2.) The difference is due to estimation/approximation error.");
Trace.WriteLine(" 3.) You may be operating along the boundary region. In general the procedure is not well defined on the boundaries. (Try gradient ascent.)");
}
}
else if (alg == "ga")
{
// Update the glide-path and recompute the probability using the new glide-path.
probnr = Climb.Run(type, @params, gp, td, wr, 2 * sn, (int)(rfMax * prec), prec, pllproc, maxgrad,
probnr, 4 * sn, grad, alpha[0]);
}
// Display the new glide-path.
Trace.WriteLine("");
Trace.Write("New Glide-Path:");
WrtAry.Run(probnr, gp, "GP", td);
// Rebuild the gradient and negate it when using NR.
maxgrad = BldGrad.Run(type, @params, gp, td, wr, 1 * sn, (int)(rfMax * prec), prec, probnr,
4 * sn, alpha[1], pllproc, grad);
if (alg == "nr")
{
for (int y = 0; y < td; ++y)
{
ngrdnt[y] = -1.00 * grad[y];
}
}
// Report the convergence status.
Trace.WriteLine("");
Trace.WriteLine($"EPSILON Convergence Criteria: {maxgrad:F15} vs. {stpthrsh:F15}");
if (maxgrad <= stpthrsh)
{
Trace.WriteLine("");
Trace.WriteLine("==========> EPSILON Convergence criteria satisfied. <==========");
}
Trace.WriteLine("");
Trace.WriteLine(new String('=', 25));
Trace.Write("End Iteration #");
Trace.WriteLine(iterint);
Trace.WriteLine(new String('=', 25));
iterint++;
}
// Build Hessian and confirm we are at a maximum, not a saddle-point or plateau for example.
Trace.WriteLine("");
Trace.WriteLine("Convergence Achieved: Final step is to confirm we are at a local/global maximum. Hessian is being built.");
hess = DrvHess.Run(type, @params, gp, td, wr, sn, (int)(rfMax * prec), prec, pllproc, grad, probnr);
hevals = new EigenvalueDecomposition(hess);
var r = hevals.RealEigenvalues;
maxeigen = r.Max();
mineigen = r.Min();
// Display the smallest/largest eigenvalues.
Trace.WriteLine("");
Trace.Write("Min Hessian eigenvalue at solution [>=0.00 --> convex region --> (local/global) minimum]: ");
Trace.WriteLine(mineigen);
Trace.WriteLine("");
Trace.Write("Max Hessian eigenvalue at solution [<=0.00 --> concave region --> (local/global) maximum]: ");
Trace.WriteLine(maxeigen);
// Write final GP to the output file.
Trace.WriteLine("");
if (maxeigen <= 0 || mineigen >= 0)
{
Trace.Write("(Local/Global) Optimal ");
}
Trace.WriteLine("Glide-Path:");
WrtAry.Run(probnr, gp, "GP", td, Path.Combine(rootdir, Config.Outfile));
Trace.WriteLine("");
}
public static double Run(string type, double[] prms, double[] a, int fxTD, double rf0, long n, int nbuckets,
int prec, double stdpnr, long npnr, double alpha, int plproc, double[] gradvctr)
{
int[] prtls = { -1, -1, -1, -1 };
double[] k = new double[fxTD];
double maxval = 0;
NormalDistribution normdist = new NormalDistribution(0.00, 1.00);
// Iterate over each time point deriving each gradient entry.
Trace.WriteLine("");
Trace.Write("Building gradient ");
for (int g = 0; g < fxTD; ++g)
{
// Construct the constant needed for gradient entries.
k[g] = Funcs.vp(prms, a[g]) / (2.00 * Funcs.v(prms, a[g])) +
Math.Pow(Funcs.mp(prms), 2) / (2.00 * Funcs.vp(prms, a[g]));
// Populate the gradient vector for this time point.
prtls[0] = g;
double grdpnr = GetPNR.Run(type, prms, a, fxTD, rf0, n, nbuckets, prec, prtls, plproc);
gradvctr[g] = k[g] * (grdpnr - stdpnr);
Trace.Write(".");
// Maximum effective absolute value of this gradient vector.
if (a[g] + gradvctr[g] > 1.00)
{
if (maxval < 1.00 - a[g])
{
maxval = 1.00 - a[g];
}
}
else if (a[g] + gradvctr[g] < Funcs.mva(prms) + 0.0001)
{
if (a[g] - (Funcs.mva(prms) + 0.0001) > maxval)
{
maxval = a[g] - (Funcs.mva(prms) + 0.0001);
}
}
else if (Math.Abs(gradvctr[g]) > maxval)
{
maxval = Math.Abs(gradvctr[g]);
}
}
Trace.WriteLine(" (Done)");
// Print the unadjusted gradient vector entries.
Trace.WriteLine("");
Trace.Write("Gradient (no adjustment):");
WrtAry.Run(-1, gradvctr, "Grd", fxTD);
// If using simulation, test each element for equality with zero. If test holds set the element to zero.
if (type == "sim" && alpha < 1.00)
{
maxval = 0;
for (int g = 0; g < fxTD; ++g)
{
double cmbpnr = (n * (stdpnr + gradvctr[g] / k[g]) + npnr * stdpnr) / (n + npnr);
double ts = (stdpnr + gradvctr[g] / k[g] - stdpnr) /
Math.Sqrt(cmbpnr * (1.00 - cmbpnr) * (1.00 / n + 1.00 / npnr));
double pval = 2.00 * Math.Min(normdist.DistributionFunction(ts),
1.00 - normdist.DistributionFunction(ts));
if (pval > alpha)
{
gradvctr[g] = 0.00; // The element is not different from zero at significance level alpha.
}
// Maximum effective absolute value of this gradient vector.
if (a[g] + gradvctr[g] > 1.00)
{
if (maxval < 1.00 - a[g])
{
maxval = 1.00 - a[g];
}
}
else if (a[g] + gradvctr[g] < Funcs.mva(prms) + 0.0001)
{
if (a[g] - (Funcs.mva(prms) + 0.0001) > maxval)
{
maxval = a[g] - (Funcs.mva(prms) + 0.0001);
}
}
else if (Math.Abs(gradvctr[g]) > maxval)
{
maxval = Math.Abs(gradvctr[g]);
}
}
// Print the adjusted gradient vector entries.
Trace.WriteLine("");
Trace.Write("ADJUSTED gradient:");
WrtAry.Run(-1, gradvctr, "Adj-Grd", fxTD);
}
// Display the maximum effective absolute value of the gradient vector (used to determine convergence).
Trace.WriteLine("");
Trace.WriteLine($"Maximum effective absolute value of this gradient: {maxval:F10}");
// This function returns the maximum absolute value of the gradient elements.
// (Which is used to define the stopping/convergence criteria.)
return(maxval);
}
