TEACHING
Seminar Series: Risk Measures and Related Stochastic Analysis (USC, Spring 2023)
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.
IE 546 Continuous-Time Finance (Spring 2024)
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.
IE 540 Financial Engineering (Spring 2021, Spring 2022)
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.
IE 523 Probabilistic Analysis (Fall 2016, Fall 2017, Fall 2018, Fall 2019, Fall 2020, Fall 2021, Fall 2023)
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.
IE 440 Introduction to Financial Engineering (Fall 2015, Spring 2017, Spring 2018, Fall 2018, Fall 2020, Fall 2021, Fall 2023)
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.
IE 421 Introduction to Stochastic Processes (Spring 2019, Spring 2021, Spring 2022, Spring 2024)
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.
IE 380 Quality Assurance and Reliability (Spring 2016, Spring 2017, Fall 2017, Spring 2018, Spring 2019, Fall 2019, Spring 2020)
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.