File size: 3,052 Bytes
5e284c8 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | #include <iostream>
#include <vector>
#include <cmath>
#include <numeric>
#include <iomanip>
// Strategy Parameters
const double T = 1.0;
const double ETA = 0.01; // alpha = eta
const double SIGMA = 0.2;
const double V_BAR = 100.0;
const int STEPS = 10000; // Discretization steps
struct Metrics {
double work;
double variance;
double probability_bound;
};
// Numerical Integration Engine
Metrics calculate_metrics(const std::vector<double>& v_path, double dt) {
double q = 0.0;
double sum_v2 = 0.0;
double sum_q2 = 0.0;
for (double v : v_path) {
// Update Inventory q_t (Riemann Sum)
q += v * dt;
// Accumulate Integrals
sum_v2 += (v * v) * dt;
sum_q2 += (q * q) * dt;
}
Metrics m;
m.work = ETA * sum_v2;
m.variance = sum_q2;
// Fluctuation Theorem: exp(-W^2 / 2*sigma^2*V)
double exponent = -std::pow(m.work, 2) / (2 * std::pow(SIGMA, 2) * m.variance);
m.probability_bound = std::exp(exponent);
return m;
}
void run_triangular() {
std::cout << "--- TRIANGULAR STRATEGY ---" << std::endl;
double dt = T / STEPS;
std::vector<double> v_path(STEPS);
// Generate Path: Buy first half, Sell second half
for (int i = 0; i < STEPS; ++i) {
double t = i * dt;
v_path[i] = (t <= T / 2.0) ? V_BAR : -V_BAR;
}
// Numerical Calculation
Metrics num = calculate_metrics(v_path, dt);
// Analytical Calculation (Paper Section 7.1)
double work_analy = ETA * std::pow(V_BAR, 2) * T;
double var_analy = (std::pow(V_BAR, 2) * std::pow(T, 3)) / 12.0;
std::cout << std::fixed << std::setprecision(4);
std::cout << "Work (Numerical): " << num.work << " | Analytical: " << work_analy << std::endl;
std::cout << "Var (Numerical): " << num.variance << " | Analytical: " << var_analy << std::endl;
std::cout << "Fluctuation Bound: " << std::scientific << num.probability_bound << std::endl << std::endl;
}
void run_ramp() {
std::cout << "--- RAMP STRATEGY ---" << std::endl;
double dt = T / STEPS;
std::vector<double> v_path(STEPS);
// Generate Path: v_t = v_bar * (T - 2t)/T
for (int i = 0; i < STEPS; ++i) {
double t = i * dt;
v_path[i] = V_BAR * (T - 2.0 * t) / T;
}
// Numerical Calculation
Metrics num = calculate_metrics(v_path, dt);
// Analytical Calculation (Paper Section 7.3 - CORRECTED)
// Work = eta * v^2 * T / 3
double work_analy = ETA * std::pow(V_BAR, 2) * T / 3.0;
// Var = v^2 * T^3 / 30
double var_analy = (std::pow(V_BAR, 2) * std::pow(T, 3)) / 30.0;
std::cout << std::fixed << std::setprecision(4);
std::cout << "Work (Numerical): " << num.work << " | Analytical: " << work_analy << std::endl;
std::cout << "Var (Numerical): " << num.variance << " | Analytical: " << var_analy << std::endl;
std::cout << "Fluctuation Bound: " << std::scientific << num.probability_bound << std::endl;
}
int main() {
run_triangular();
run_ramp();
return 0;
}
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