feat: Add Kelly Criterion and Sharpe Ratio financial algorithms

[realsamrat]

Description

This PR adds two new financial algorithm implementations to the financial/ directory:

1. Kelly Criterion (kelly_criterion.py)

The Kelly Criterion is a formula for optimal position sizing in betting and trading, developed by John L. Kelly Jr. in 1956. It determines the optimal fraction of capital to risk on a bet or investment to maximize long-term growth.

Functions implemented:

• kelly_criterion(win_probability, win_loss_ratio) - Basic Kelly formula
• kelly_criterion_extended(win_probability, win_amount, loss_amount) - General form with explicit amounts
• fractional_kelly(win_probability, win_loss_ratio, fraction) - Fractional Kelly (e.g., half-Kelly) for reduced volatility

Applications:

• Sports betting and gambling strategy
• Investment portfolio sizing
• Trading position management

2. Sharpe Ratio (sharpe_ratio.py)

The Sharpe Ratio measures risk-adjusted returns, developed by Nobel laureate William F. Sharpe. It calculates excess return per unit of risk (standard deviation).

Functions implemented:

• sharpe_ratio(returns, risk_free_rate) - Basic Sharpe Ratio calculation
• annualized_sharpe_ratio(returns, risk_free_rate, periods_per_year) - Annualized version for different time periods

Applications:

• Portfolio performance comparison
• Mutual fund and hedge fund evaluation
• Trading strategy assessment

References

• Kelly Criterion: https://en.wikipedia.org/wiki/Kelly_criterion
• Sharpe Ratio: https://en.wikipedia.org/wiki/Sharpe_ratio

Testing

✅ All doctests pass:

• python -m doctest financial/kelly_criterion.py -v - 22/22 tests passed
• python -m doctest financial/sharpe_ratio.py -v - 14/14 tests passed

Both files follow TheAlgorithms style guide:

• Complete docstrings with formula explanations
• Comprehensive doctests including edge cases
• Type hints on all functions
• Pure Python (no external dependencies)
• Input validation with appropriate error messages

Checklist

• Added comprehensive doctests with edge cases
• Type hints on all parameters and return values
• No external dependencies (pure Python stdlib)
• Follows existing code style in financial/ directory
• All doctests pass
• Includes Wikipedia and Investopedia references