Martingales and optional stopping

Discrete-time martingales, sub- and supermartingales: convergence theorems (almost sure, L^p, backwards, Lévy's downward theorem), uniform integrability, Doob's maximal inequalities, orthogonality and conditional variance of increments, optional stopping in all its forms, and Wald's equations for stopped sums. Martingale measures and the fundamental theorem of asset pricing.

• Backwards martingales and Lévy's downward theorem
• Convex functions of martingales
• Doob's maximal inequalities
• Fundamental theorem of asset pricing
• Martingale convergence theorems
• Optional stopping theorem
• Square-integrable martingales
• Wald's equations

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