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zhutoutoutousan
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"""
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Martingale Strategy Simulation
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Analyzes the statistical properties and risk of martingale strategies
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"""
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import numpy as np
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import matplotlib
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matplotlib.use('Agg') # Use non-interactive backend
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import matplotlib.pyplot as plt
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from scipy import stats
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import pandas as pd
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class MartingaleSimulator:
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def __init__(self, initial_balance=10000, base_lot=0.01, win_prob=0.5,
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win_amount=10, loss_amount=10, max_losses=10):
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self.initial_balance = initial_balance
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self.base_lot = base_lot
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self.win_prob = win_prob
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self.win_amount = win_amount
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self.loss_amount = loss_amount
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self.max_losses = max_losses
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def calculate_position_size(self, consecutive_losses):
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"""Calculate position size after n consecutive losses"""
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return self.base_lot * (2 ** consecutive_losses)
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def calculate_required_capital(self, consecutive_losses):
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"""Calculate total capital needed after n losses"""
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return self.base_lot * (2 ** (consecutive_losses + 1) - 1)
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def simulate_trade_sequence(self, num_trades=1000):
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"""Simulate a sequence of trades"""
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balance = self.initial_balance
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consecutive_losses = 0
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trades = []
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ruin = False
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for i in range(num_trades):
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if balance <= 0:
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ruin = True
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break
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# Calculate position size
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position_size = self.calculate_position_size(consecutive_losses)
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required_capital = self.calculate_required_capital(consecutive_losses)
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# Check if we have enough capital
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if required_capital > balance:
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ruin = True
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break
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# Simulate trade outcome
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is_win = np.random.random() < self.win_prob
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if is_win:
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# Win: recover all previous losses
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profit = position_size * self.win_amount
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balance += profit
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consecutive_losses = 0
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outcome = 'Win'
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else:
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# Loss: add to consecutive losses
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loss = position_size * self.loss_amount
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balance -= loss
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consecutive_losses += 1
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outcome = 'Loss'
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trades.append({
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'trade': i + 1,
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'balance': balance,
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'position_size': position_size,
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'consecutive_losses': consecutive_losses,
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'outcome': outcome,
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'profit': profit if is_win else -loss
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})
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return pd.DataFrame(trades), ruin
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def monte_carlo_analysis(self, num_simulations=1000, num_trades=100):
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"""Run Monte Carlo simulation"""
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results = []
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ruin_count = 0
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for sim in range(num_simulations):
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trades_df, ruin = self.simulate_trade_sequence(num_trades)
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if ruin:
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ruin_count += 1
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final_balance = 0
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else:
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final_balance = trades_df['balance'].iloc[-1]
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results.append({
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'simulation': sim,
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'final_balance': final_balance,
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'ruin': ruin,
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'total_trades': len(trades_df),
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'max_consecutive_losses': trades_df['consecutive_losses'].max() if len(trades_df) > 0 else 0
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})
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return pd.DataFrame(results), ruin_count / num_simulations
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def plot_simulation_results(self, num_simulations=100):
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"""Plot simulation results"""
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fig, axes = plt.subplots(2, 2, figsize=(15, 10))
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# Run simulations
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results_df, ruin_prob = self.monte_carlo_analysis(num_simulations)
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# Plot 1: Final Balance Distribution
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axes[0, 0].hist(results_df['final_balance'], bins=50, edgecolor='black')
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axes[0, 0].axvline(self.initial_balance, color='red', linestyle='--',
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label=f'Initial Balance: ${self.initial_balance:,.0f}')
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axes[0, 0].set_xlabel('Final Balance ($)')
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axes[0, 0].set_ylabel('Frequency')
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axes[0, 0].set_title(f'Final Balance Distribution\nRuin Probability: {ruin_prob:.2%}')
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axes[0, 0].legend()
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axes[0, 0].grid(True, alpha=0.3)
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# Plot 2: Ruin Probability vs Consecutive Losses
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max_losses_range = range(1, self.max_losses + 1)
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ruin_probs = []
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for n in max_losses_range:
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required = self.calculate_required_capital(n)
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ruin_probs.append(1.0 if required > self.initial_balance else 0.0)
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axes[0, 1].plot(max_losses_range, ruin_probs, 'ro-', linewidth=2, markersize=8)
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axes[0, 1].set_xlabel('Consecutive Losses')
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axes[0, 1].set_ylabel('Ruin Probability')
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axes[0, 1].set_title('Ruin Probability vs Consecutive Losses')
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axes[0, 1].grid(True, alpha=0.3)
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axes[0, 1].set_ylim([-0.1, 1.1])
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# Plot 3: Position Size Growth
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losses_range = range(0, self.max_losses + 1)
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position_sizes = [self.calculate_position_size(n) for n in losses_range]
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required_capital = [self.calculate_required_capital(n) for n in losses_range]
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ax3_twin = axes[1, 0].twinx()
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line1 = axes[1, 0].plot(losses_range, position_sizes, 'b-o',
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label='Position Size', linewidth=2)
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line2 = ax3_twin.plot(losses_range, required_capital, 'r-s',
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label='Required Capital', linewidth=2)
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axes[1, 0].set_xlabel('Consecutive Losses')
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axes[1, 0].set_ylabel('Position Size (Lots)', color='b')
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ax3_twin.set_ylabel('Required Capital ($)', color='r')
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axes[1, 0].set_title('Position Size and Capital Requirements')
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axes[1, 0].grid(True, alpha=0.3)
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# Combine legends
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lines = line1 + line2
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labels = [l.get_label() for l in lines]
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axes[1, 0].legend(lines, labels, loc='upper left')
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# Plot 4: Sample Trade Sequence
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sample_trades, _ = self.simulate_trade_sequence(50)
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axes[1, 1].plot(sample_trades['trade'], sample_trades['balance'],
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'g-', linewidth=2, label='Balance')
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axes[1, 1].axhline(self.initial_balance, color='red', linestyle='--',
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label='Initial Balance')
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axes[1, 1].set_xlabel('Trade Number')
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axes[1, 1].set_ylabel('Balance ($)')
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axes[1, 1].set_title('Sample Trade Sequence (50 trades)')
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axes[1, 1].legend()
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axes[1, 1].grid(True, alpha=0.3)
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plt.tight_layout()
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return fig
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if __name__ == "__main__":
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# Create simulator
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simulator = MartingaleSimulator(
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initial_balance=10000,
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base_lot=0.01,
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win_prob=0.5,
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win_amount=10,
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loss_amount=10,
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max_losses=10
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)
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# Run analysis
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print("Running Martingale Simulation...")
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results_df, ruin_prob = simulator.monte_carlo_analysis(num_simulations=1000, num_trades=100)
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print(f"\n=== Martingale Strategy Analysis ===")
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print(f"Initial Balance: ${simulator.initial_balance:,.2f}")
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print(f"Win Probability: {simulator.win_prob:.1%}")
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print(f"\nMonte Carlo Results (1000 simulations):")
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print(f"Ruin Probability: {ruin_prob:.2%}")
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print(f"Mean Final Balance: ${results_df['final_balance'].mean():,.2f}")
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print(f"Median Final Balance: ${results_df['final_balance'].median():,.2f}")
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print(f"Std Dev Final Balance: ${results_df['final_balance'].std():,.2f}")
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print(f"Max Final Balance: ${results_df['final_balance'].max():,.2f}")
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print(f"Min Final Balance: ${results_df['final_balance'].min():,.2f}")
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# Calculate statistics
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profitable_sims = (results_df['final_balance'] > simulator.initial_balance).sum()
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print(f"\nProfitable Simulations: {profitable_sims}/{len(results_df)} ({profitable_sims/len(results_df):.1%})")
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print(f"Average Max Consecutive Losses: {results_df['max_consecutive_losses'].mean():.2f}")
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# Generate plots
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import os
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# Get the script directory and construct path to figures
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script_dir = os.path.dirname(os.path.abspath(__file__))
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figures_dir = os.path.join(script_dir, '..', 'figures')
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figures_path = os.path.abspath(figures_dir)
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os.makedirs(figures_path, exist_ok=True)
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fig = simulator.plot_simulation_results(num_simulations=100)
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output_path = os.path.join(figures_path, 'martingale_analysis.png')
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plt.savefig(output_path, dpi=300, bbox_inches='tight')
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print(f"\nFigure saved to {output_path}")
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plt.close()
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