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// Copyright (C) 2017 EDF
// All Rights Reserved
#include <memory>
#include <iostream>
#include <Eigen/Dense>
#include "StOpt/regression/BaseRegression.h"
#include "StOpt/core/grids/SpaceGrid.h"
#include "StOpt/core/grids/Interpolator.h"
#include "StOpt/core/utils/constant.h"
using namespace Eigen;
using namespace std;
using namespace StOpt;
std::pair<ArrayXd, ArrayXXd> globalL2HedgeMinimize(const ArrayXXd &p_difS,
const Eigen::ArrayXXd &p_asset,
const ArrayXd &p_delta,
const Eigen::ArrayXd &p_spread1,
const Eigen::ArrayXd &p_spread2,
const SpaceGrid &p_commandGrid,
const shared_ptr< BaseRegression > &p_regressor,
const SpaceGrid &p_gridNext,
const ArrayXXd &p_hMinusGainNext)
{
int nbSim = p_regressor->getParticles().cols();
// to store the minimization value calculated per simulation
ArrayXd minVar = ArrayXd::Constant(nbSim, infty);
// store the hedge
ArrayXXd hedge(p_delta.size(), nbSim);
ArrayXd hMinusGain = ArrayXd::Constant(nbSim, infty);
shared_ptr<GridIterator> iterGrid = p_commandGrid.getGridIterator();
while (iterGrid->isValid())
{
// next position to test
Eigen::ArrayXd deltaNext = iterGrid->getCoordinate();
// get interpolator associated to grid at the next time
shared_ptr<Interpolator> interpolator = p_gridNext.createInterpolator(deltaNext);
// interpolate (H-G) at the position at next date
ArrayXd hMinGInterp = interpolator->applyVec(p_hMinusGainNext);
// (H-G) at the next and subtract trading gains
ArrayXd currentHMGain = hMinGInterp - (p_difS.matrix().transpose() * deltaNext.matrix()).array() ;
// spread by quantity
ArrayXd dQuantAbs = (deltaNext - p_delta).abs();
ArrayXd spreadQuant1 = p_spread1 * dQuantAbs;
ArrayXd spreadQuant2 = p_spread2 * dQuantAbs;
// to H-G add transaction cost
currentHMGain += spreadQuant1.sum();
currentHMGain += (p_asset.matrix().transpose() * spreadQuant2.matrix()).array();
// calculate conditional expectation for this command
ArrayXd espHMGain = p_regressor->getAllSimulations(currentHMGain);
// now do the arbitrage cell by cell by conditional expectation
ArrayXd diffSquaredEsp = p_regressor->getAllSimulations((currentHMGain - espHMGain).pow(2.));
// arbitrage
for (int isim = 0; isim < nbSim; ++isim)
{
if (diffSquaredEsp(isim) < minVar(isim))
{
hedge.col(isim) = deltaNext;
minVar(isim) = diffSquaredEsp(isim);
hMinusGain(isim) = currentHMGain(isim);
}
}
iterGrid->next();
}
return make_pair(hMinusGain, hedge.transpose());
}
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