Approach 2 Sharpe Ratio Maximization

Using the guessing accuracy as reward function is not the same as maximizing profiting. since we have high probability than theatrical average. we should consider building a rewarding function that invest in window.

That is an excellent point and a critical realization in quantitative finance: Accuracy \(\neq\) Profitability. An agent could be \(90\%\) accurate but lose money if its few wrong predictions lead to massive losses (i.e., poor risk management).

Your thinking is absolutely correct: we need a reward function that directly models Expected Value (EV) maximization over a series of trades, which is exactly the core principle of a casino's mechanics.

My Recommendation: Approach 2 (Sharpe Ratio Maximization)¶

While Approach 1 (Log Returns) is a strong foundation, Approach 2: Sharpe Ratio Maximization is arguably the best single metric for translating the "casino mechanic" of low-volatility, consistent profit into a machine learning objective.

Rationale for Sharpe Ratio (Approach 2):¶

Risk-Adjusted Return: The Sharpe Ratio (\(\text{Sharpe} = \frac{\text{Return}}{\text{Volatility}}\)) forces the agent to maximize return while simultaneously minimizing the volatility (risk) required to achieve that return.
Consistency Focus: A strategy that makes many small, consistent profits will have a very high Sharpe Ratio. A strategy that makes large, infrequent profits but has many "noise" trades will have a low Sharpe Ratio due to high volatility.
Casino Analogy: A casino aims for a predictable, steady, low-variance income stream. The Sharpe Ratio is the metric that best captures this "predictable income" goal for a financial strategy.

Proposed Strategy: Sharpe-Optimized Fixed-Fractional Trading¶

We will combine the Fixed-Fractional Trading mechanics (from the previous discussion) with the Sharpe Ratio as the reward.

1. Investment Strategy:¶

Fixed Allocation: Assume the agent is always \(100\%\) allocated when a Buy/Sell signal is given, and \(100\%\) in cash on a Hold signal.
Target: The agent's goal is to generate a time series of returns that has the highest possible mean (profit) relative to its standard deviation (risk) over the training period.

2. The New Reward Function (`get_reward`)¶

The reward will be the calculated Sharpe Ratio of the simulated daily returns (P&L series) generated by the proposed weights.

def get_reward_sharpe_ratio(self, weights):
    self.model.set_weights(weights)

    # 1. Simulate the daily returns series for the training period
    returns_series = []

    # Simple, ignored transaction cost C = 0.0005 (0.05%)
    TRANSACTION_COST = 0.0005 

    for t in range(self.train_start, self.train_end - 1):
        state = self.get_state(t)
        action = self.act(state) 

        current_price = self.trend[t]
        next_price = self.trend[t + 1]
        simple_return = (next_price - current_price) / current_price

        daily_return = 0.0 # Default return for Hold

        if action == 1: # Buy (Go Long)
            # Daily Return = Simple Return - Transaction Cost
            daily_return = simple_return - TRANSACTION_COST

        elif action == 2: # Sell (Go Short)
            # Daily Return = Negative of Simple Return - Transaction Cost
            daily_return = -simple_return - TRANSACTION_COST

        # Action 0 (Hold): daily_return remains 0.0

        returns_series.append(daily_return)

    # 2. Convert to numpy array for statistics
    returns = np.array(returns_series)

    # 3. Calculate Mean and Standard Deviation (Risk-Free Rate is 0)
    mean_return = np.mean(returns)
    std_dev = np.std(returns)

    # 4. Calculate the Sharpe Ratio
    # Add a small epsilon to avoid division by zero (for zero-volatility)
    sharpe_ratio = mean_return / (std_dev + 1e-6)

    return sharpe_ratio

Why this is a "Better" Casino Strategy:¶

The agent is now trained to find patterns that result in a high \(\text{Mean Return}\) AND a low \(\text{Standard Deviation}\) of those returns.
It will actively avoid high-volatility trades, even those with a positive expected value, if they disproportionately increase the denominator (risk).
The transaction cost ensures the agent is only rewarded for trades that achieve an edge greater than the cost, reinforcing the need for a truly positive EV signal.

This approach provides a direct, single, and robust metric for optimizing the "consistent, low-variance profit" (casino) strategy.