Stochastic Calculus Finance

objective

Apply stochastic calculus theory to finance models with rigorous measure and martingale checks.

workflow

1. define probability space, filtrations, and process assumptions.
2. derive pricing dynamics under physical and risk-neutral measures.
3. validate no-arbitrage conditions and martingale properties.
4. connect theoretical results to implementable pricing formulas.
5. approve model only after theorem assumptions are explicitly verified.

required diagnostics

• martingale tests under chosen numeraire.
• measure-change consistency diagnostics.
• boundary-condition and transversality checks.
• analytical-versus-numerical valuation parity.
• assumption-violation impact analysis.