Monte Carlo simulation is a powerful computational method that uses random sampling to solve complex financial problems, particularly in portfolio optimization where analytical solutions may be intractable.

The method involves random sampling by generating scenarios based on probability distributions, statistical analysis by examining outcomes across thousands or millions of scenarios, risk assessment by quantifying uncertainty and probability of outcomes, and informed decision making based on probabilistic analysis.

Applications include projecting portfolio returns under various market conditions, calculating risk metrics like VaR and Expected Shortfall, assessing likelihood of meeting investment goals, and building robust portfolios that perform well across diverse scenarios.