TEACHING

Graduate level seminar series on risk measures. Topics include static univariate risk measures, primal and dual representations, dynamic risk measures, time-consistency, risk measures and backward stochastic differential equations, set-valued risk measures, systemic risk with some supplementary lectures on Banach spaces, topological vector spaces, and convexity.

Graduate level elective course on stochastic calculus and financial applications. Topics include martingales in discrete time, Brownian motion, martingales in continuous time, stochastic integration, localization, Itô's formula, Girsanov's theorem, martingale representation theorem, stochastic differential equations, Black-Scholes model.

Graduate level elective course on financial engineering. Topics include fundamental theorems of asset pricing in static and discrete-time settings, static and dynamic risk measures, set-valued risk measures, systemic risk with some supplementary lectures on Banach spaces, topological vector spaces, and convexity.

Graduate level required course on probability theory. Topics include measure and probability spaces,  construction of measures, monotone class theorem, measurable functions, Lebesgue integrals, expectations, Laplace and Fourier transforms, product spaces, multivariate distributions, conditioning, transition kernels, modes of convergence, laws of large numbers, central limit theorem.

Video lectures from Fall 2017 are available on YouTube.

Senior level elective course on financial engineering. Topics include portfolio optimization, capital asset pricing model, bonds, forward and futures contracts, options, binomial model, general models in discrete time, fundamental theorems of asset pricing and their proofs in static setting, Brownian motion, Itô’s formula, Black-Scholes model, hedging with Greek letters, mean reversion.

Senior level elective course on stochastic processes. Topics include probability spaces, random vectors, conditional expectations, filtrations, stopping times, Bernoulli processes, Poisson processes, random walks, discrete-time martingales, Brownian motion, Gaussian processes, continuous-time martingales.

Junior level required course on quality engineering. Topics include quality philosophies, statistical process control, process capability analysis, reliability theory, analysis of variance, experimental design, Taguchi’s orthogonal arrays, acceptance sampling.