Teaching

University of Verona

Lecturer

Constrained Optimization: the Weierstrass Theorem. Constrained optimization with equality
 constraints, Lagrange theorem. Lagrangian function and optimality conditions. Constrained
optimization with inequality constraints, Kuhn-Tucker theorem. Convex problems.

University of Oxford


Class Tutor (third-year undergraduates and Masters students)



Arbitrage and the law of one price, Binomial model for European and American options, continuous-time martingales, Itô's formula and SDEs, Black-Scholes analysis, Feynman-Kac and risk neutral pricing, free-boundary problem for American options, simple exotic options (barriers, lookbacks and Asians), implied volatility.



American options (obstacle problems), PDEs for multi-factor models, calibration of volatility models to quoted market prices.



Basic measure theory, Radon-Nikodym Theorem, L^p convergence, Uniform Integrability, Conditional Expectation, Filtrations and stopping times, Martingales in discrete-time, Optimal stopping theorem, Maximal inequalities, Upcrossing lemmas.



College Tutorials (Magdalen College) 



General linear homogeneous ODEs,  integrating factor, first and second order linear ODEs with constant coefficients, partial derivatives, multivariable chain rule, parametric representation of curves, line integrals, Jacobians, gradient vector, directional derivative, Taylor's Theorem, classification of Critical points, Lagrange multipliers.



Volume integrals: Jacobians for cylindrical and spherical polars. Flux integrals including solid angle. Work integrals and conservative fields. Divergence and curl. Divergence theorem, Green's first and second theorems. Stokes's theorem. Gauss' Flux Theorem.


Teaching Assistant