Archives

Here you can find all of the things I wrote over the past few years. I do not guarantee that any of these are correct or accurate, either as a whole or in part:

Quantitative Finance

• Monte Carlo estimation using Variance Reduction.: This is a tiny note I wrote as part of the CQF. I briefly compare variance reduction techniques such as geometric, arithmetic and importance sampling.
• Statistical Arbitrage using Time Series Analysis: As part of the final project in the Certificate in Quantitative Finance (CQF) on algorithmic trading, I implemented and backtested a pairs trading strategy. Features of this strategy included: 1) Identifying and estimating a cointegrated relationship between two time series, through OLS regression, and by applying the Engle-Granger procedure on the residuals. Also considered the Johansen procedure. 2) After establishing cointegration, fitting an Ornstien-Uhlenbeck process to the spread for identifying entry and exit points of trading. 3) Backtesting of this strategy using the R package 'quantstrat'. Additionally, the final project had a mandatory component of calculating Credit Valuation Adjustment (CVA) for an Interest Rate Swap.
• Topological Data Analysis

• Topological Data Analysis of Financial Time Series : For a reading seminar at the UWO, I implemented TDA on various time series data. The slides contain the results. Here is the R code accompanying the talk.
• Differential Geometry

• The Baker-Campbell-Hausdroff Formula: A (half-hearted) expository account of Lie Theory and the Baker-Campbell-Hausdorff formula. The main source for this was Terry Tao's blog posts.
• Dessins d'enfant

• Belyi's theorem and Dessin d'enfant: Another expository article on dessins d'enfant.
• Harmonic Analysis

• On certain group theoretic aspects of the Fourier Transform.: My master's thesis (if you could call it that), consisted of me dissecting the definition of the Fourier transform to see how the different pieces generalize. Heavily inspired by Folland's book on Abstract Harmonic Analysis.
• Wavelets on Local Fields: Structure theory of local fields and defining Wavelets on them through Multiresolution Analysis.
• Homotopy Type Theory

• Voevodsky's construction of a universe in the Simplicial Model of HoTT.: Notes for a talk at the CMU HoTT seminar, where I outline Voevodsky's construction of a contextual category from a universe object. Also sketched is a proof of the universe map being a Kan fibration.
• Homotopy Theory

• A big-picture overview of Simplicial,Stable and Local Homotopy Theory. : These notes were taken and written up following Rick Jardine's course on Homotopy Theory at the University of Western Ontario.