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#include <iostream>
#include <fstream>
#include <vector>
#include <gsl/gsl_cdf.h>
#include <gsl/gsl_math.h>
#include "stratified_sampling.hpp"
#include <cmath>
#include <algorithm>
#include "opti.hpp"
#include "option.hpp"
#include "rqmc.hpp"
using namespace std;
struct first:public std::unary_function<std::vector<double>, double>
{
double operator()(std::vector<double> X){
return X[0];
}
};
vector< vector<double> > exemple1_stratified() {
int I = 10; //le nombre de strates
vector<double> q = quantile_norm(10, 1);
vector<double> p(I, 1/(double)I);
vector<gaussian_truncated> rvar;
rvar.push_back(gaussian_truncated(GSL_NEGINF, q[0]));
for (int i=1; i<I; i++){
rvar.push_back(gaussian_truncated(q[i-1], q[i]));
};
vector<int> N = {300, 1000, 10000, 20000}; //notre tableau du nombre successif de tirages, qui correspondent aux 300, 1300, 11300 et 31300
//de l'article de Etoré et Jourdain
vector< vector<double> > data (4);
stratified_sampling<gaussian_truncated> S(p,rvar);
cout<<"N"<<"\t"<<"moyenne"<<"\t\t"<<"sigma"<<"\t"<<"théorique"<<endl;
vector<double> r(4,0);
for (size_t i=0; i<N.size(); i++){
S.draw(N[i]);
r[0]= r[0] + N[i];
r[1] = S.estimator().first;
r[2] = S.estimator().second;
r[3] = 0.1559335;
cout<<r[0]<<"\t"<<r[1]<<"\t"<<r[2]<<"\t"<<r[3]<<endl;
data[i] = r;
};
return data;
};
vector< vector<double> > exemple1_rqmc(){
int I = 100;
vector<int> N = {3, 13, 113, 313}; //les N choisis pour que les NI soient égaux aux N de l'exemple 1 stratified_sampling
first f; //comme quasi_gaussian retourne un vecteur, on doit composer avec f pour avoir le double QG()[0]
vector< vector<double> > data (4);
for(size_t i =0; i<N.size(); i++){
data[i] = monte_carlo (I, quasi_mean<struct first, sobol> (N[i], 1, f));
}
cout<<"moyenne"<<"\t\t"<<"sigma"<<"\t\t"<<"taille IC"<<endl;
for(int i =0; i<3; i++){
cout<<data[i][0]<<"\t"<<data[i][1]<<"\t"<<data[i][2]<<endl;
}
return data;
};
std::vector<double> normalize (std::vector<double> mu) {
double norm_mu = accumulate(mu.begin(), mu.end(), 0.,
[](double x, double y){ return x + y*y;});
vector<double> u(mu);
transform(u.begin(), u.end(), u.begin(), [norm_mu](double x){ return x/sqrt(norm_mu); });
return u;
}
vector <vector<double> > exemple2_stratified (int d, bool call = true){
vector<double> K = {45, 50, 55};
vector<int> N = {100000, 400000, 500000};
int I = 100; //le nombre de strates
vector< vector<double> > data(3);
vector<double> q = quantile_norm(I, 1);
vector<double> p(I, 1/(double)I);
double r = 0.05;
double T = 1.0;
double S0 = 50;
double V = 0.1;
typedef compose_t<exponential_tilt<asian_option>, multi_gaussian_truncated> tilted_option;
for (size_t i=0; i < K.size(); i++){
vector<double> mu = argmax(r, T, S0, V, K[i], d, call);
std::vector<double> u = normalize(mu);
asian_option A(r, T, S0, V, K[i], call);
exponential_tilt<asian_option> G(mu, A);
std::vector<tilted_option> X;
X.push_back(compose(G, multi_gaussian_truncated(GSL_NEGINF, q[0], u)));
for(int j=1; j < I; j++) {
X.push_back(compose(G, multi_gaussian_truncated(q[j-1], q[j], u)));
}
stratified_sampling<tilted_option> S(p, X);
vector<double> r(3, 0);
for (size_t j=0; j < N.size(); j++){
S.draw(N[j]);
}
r[0] = K[i];
r[1] = S.estimator().first;
r[2] = S.estimator().second;
data[i] = r;
}
return data;
}
vector< vector<double> > exemple2_rqmc(int d, bool call = true) {
int N= 10000;
double r = 0.05;
double T = 1.0;
double S0 = 50;
double V = 0.1;
vector< vector<double> > data(3);
vector<double> K = {45, 50, 55};
int I=100;//la taille du vrai Monte-Carlo
for(int i =0; i<3; i++) {
asian_option A(r, T, S0, V, K[i], call);
data[i] = monte_carlo(I, quasi_mean<asian_option, sobol> (N, d, A));
}
return data;
};
int make_table1(vector< vector<double> > const &data1, vector< vector<double> > const &data2) {
std::fstream fs("doc/table1.tex", std::fstream::out);
fs<<R"(\begin{tabular}{|r|rr|rr|c|})"<<std::endl;
fs<<R"(\hline)"<<endl;
fs<<"N"<<" & "<<R"($\mu_{strat}$)"<<" & "<<R"($\mu_{rqmc}$)"<<" & "<<R"($\textrm{IC}_{strat}$)"<<" & "<<R"($\textrm{IC}_{rqmc}$)"<<" & "<< R"($\textrm{IC}_{strat}/\textrm{IC}_{rqmc}$)"<<R"(\\ \hline)"<<std::endl;
fs.precision(2);
for (int i=0; i< 4; i++) {
double ic_strat = 1.95996*sqrt(data1[i][2]/(double) data1[i][0]);
fs<<(int)data1[i][0]<<"&"<<scientific<<data1[i][1]<<"&"<<data2[i][0]<<"&"<<ic_strat<<"&"<<data2[i][2]/2<<"&"<<fixed<<ic_strat/(data2[i][2]/2)<<R"(\\ \hline)"<<std::endl;
}
fs<<R"(\end{tabular})"<<std::endl;
fs.close();
return 0;
}
int make_table2(vector< vector<double> > data1, vector< vector<double> > data2, vector< vector<double> > data3, vector< vector<double> > data4, string table_name) {
std::fstream fs("doc/" + table_name, std::fstream::out);
fs<<R"(\begin{tabular}{|r|r|rr|rr|c|})"<<std::endl;
fs<<R"(\hline)"<<endl;
fs<<"d"<<" & "<<"K"<<" & "<<R"($\mu_{strat}$)"<<" & "<<R"($\mu_{rqmc}$)"<<" & "<<R"($\textrm{IC}_{strat}$)"<<" & "<<R"($\textrm{IC}_{rqmc}$)"<<" & "<< R"($\textrm{IC}_{strat}/\textrm{IC}_{rqmc}$)"<<R"(\\ \hline)"<<std::endl;
fs.precision(3);
int N = 1000000;
for (int i=0; i< 3; i++) {
double ic_strat = 1.95996*sqrt(data1[i][2]/(double) N);
fs<<"16"<<" & "<< (int) (data1[i][0]) <<"&"<< fixed <<data1[i][1] <<" & "<<data2[i][0]<<" & "<< scientific <<ic_strat<<" & "<<data2[i][2]/2<<" & "<<fixed<<ic_strat/(data2[i][2]/2)<<R"(\\)"<<std::endl;
}
fs<<R"(\hline\hline)"<<endl;
for (int i=0; i< 3; i++) {
double ic_strat = 1.95996*sqrt(data3[i][2]/(double) N);
fs<<"64"<<" & "<< (int) (data3[i][0]) <<"&"<< fixed << data3[i][1] <<" & "<<data4[i][0]<<" & "<< scientific <<ic_strat<<" & "<<data4[i][2]/2<<" & "<<fixed<<ic_strat/(data4[i][2]/2)<<R"(\\)"<<std::endl;
}
fs<<R"(\hline)"<<endl;
fs<<R"(\end{tabular})"<<std::endl;
fs.close();
return 0;
}
int main()
{
init_alea(0);
cout<<"comparaison stratified sampling/RQMC sur l'example 1\n"<<endl;
make_table1(exemple1_stratified(), exemple1_rqmc());
vector< vector<double> > data1 = exemple2_stratified(16);
vector< vector<double> > data2 = exemple2_rqmc(16);
vector< vector<double> > data3 = exemple2_stratified(64);
vector< vector<double> > data4 = exemple2_rqmc(64);
make_table2(data1, data2, data3, data4, "table2.tex");
vector< vector<double> > data5 = exemple2_stratified(16, false);
vector< vector<double> > data6 = exemple2_rqmc(16, false);
vector< vector<double> > data7 = exemple2_stratified(64, false);
vector< vector<double> > data8 = exemple2_rqmc(64,false);
make_table2(data5, data6, data7, data8, "table3.tex");
return 0;
}
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