Students will learn basic concepts of probability spaces: -algebras, distributions, proba-
bility densities, independence, conditional expectations.
2. Students will learn the Brownian Motion, Wiener measure, Stochastic processes, and Ito's
3. Students will learn Stochastic di
erential equations, di
usion processes, Markov proper-
ties, Kolmogorov's backward equation, the generator of an Ito di
usion, boundary value
problems, the Dirichlet problem, the Poisson problem, and the Girsanov theorem.
4. Students will learn financial markets with mathematical interpretations, portfolio and
arbitrage, attainability and completeness, Black-Scholes equation and its solution formula,
and European options.
5. Students will learn optimal stopping theory, American options, PDEs with free boundaries,
and variational inequalities.