Risk of ruin sounds academic, but it is the correct language for a common retail failure mode: you sized too large relative to drawdown tolerance, then a normal losing streak ended the account.

Exact closed-form solutions rarely match reality because returns are not IID and leverage is nonlinear.

The operational definition

Pick a ruin threshold:

account equity below X dollars
or drawdown beyond Y percent where you must stop trading

Risk of ruin is the probability you hit that threshold before your process recovers.

Practical estimation without pretending you are a casino

Instead of fragile formulas, use a Monte Carlo or bootstrap simulator that respects:

fat tails
volatility clustering
your actual position sizing rule
fees and slippage

Then simulate many paths and measure the fraction that cross the ruin threshold.

The real lever: position sizing and stop-trading rules

Most "ruin" is not Gaussian noise. It is:

leverage + liquidation
one broken execution path
one strategy bug

So the strongest interventions are operational:

cap leverage
cap per-strategy drawdown budgets
automated kill-switch on execution drift

Why "edge percentage" is not enough without path risk

Even positive expectancy processes can hit ruin thresholds if:

bet sizing grows with short-term performance
leverage is dynamic
drawdown constraints are soft

If your simulator assumes static sizing but you scale up after wins, your modeled ruin risk is fiction.

A practical Monte Carlo recipe (high level)

build daily or trade-by-trade return series from OOS periods (preferred) or stressed IS
resample blocks to preserve volatility clustering
apply your real sizing rule and fee model
count paths that hit the ruin threshold

Repeat with stressed costs. If ruin probability jumps orders of magnitude, your edge was partly a liquidity illusion.

Ruin is a joint statement about edge, variance, and discipline

Improving only the model while loosening sizing rules can increase ruin risk even if backtest returns rise.