The course covers: the Feynman-Kac formula and the Fokker-Plank equation, stochastic calculus with jumps, Levy processes and jump diffusion models in finance, Bellman's principle of dynamic programming and the Hamilton-Jacobi- Bellman equation, classical problems for optimal control in finance (Merton's problem, etc.), investment-consumption decisions with transaction costs, the connection between asset pricing and free-boundary problems for PDEs, optimal stopping problems and the exercise of American-style derivatives, capital structure and valuation of real options and corporate debt, exchange options, stochastic volatility models, and Dupire's formula. (Mathematical Finance courses are reserved for students enrolled in the Mathematical Finance program.)