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% The standard font packages \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % For neatly defining theorems and definitions %\usepackage{amsthm} % Including EPS/PDF graphics (\includegraphics) %\usepackage{graphicx} % Making matrix-based graphics %\usepackage{xypic} % Enumeration lists with different styles %\usepackage{enumerate} % Set up the theorem environments %\newtheorem{thm}{Theorem} %\newtheorem*{thm*}{Theorem} \newcommand{\defnterm}[1]{\emph{#1}} % The standard number systems \newcommand{\complex}{\mathbb{C}} \newcommand{\real}{\mathbb{R}} \newcommand{\rat}{\mathbb{Q}} \newcommand{\nat}{\mathbb{N}} \newcommand{\intset}{\mathbb{Z}} % Absolute values and norms % Normal, wide, and big versions of the delimeters \newcommand{\abs}[1]{\lvert#1\rvert} \newcommand{\absW}[1]{\left\lvert#1\right\rvert} \newcommand{\absB}[1]{\Bigl\lvert#1\Bigr\rvert} \newcommand{\norm}[1]{\lVert#1\rVert} \newcommand{\normW}[1]{\left\lVert#1\right\rVert} \newcommand{\normB}[1]{\Bigl\lVert#1\Bigr\rVert} % Inverse functions \newcommand{\inv}[1]{{#1}^{-1}} % Differentiation operators \newcommand{\od}[2]{\frac{d #1}{d #2}} \newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\pdd}[2]{\frac{\partial^2 #1}{\partial #2}} \newcommand{\ipd}[2]{\partial #1 / \partial #2} % Differentials on integrals \newcommand{\dx}{\, dx} \newcommand{\dt}{\, dt} \newcommand{\dmu}{\, d\mu} % Inner products \newcommand{\ip}[2]{\langle {#1}, {#2} \rangle} % Complex numbers \DeclareMathOperator{\zRe}{Re} \DeclareMathOperator{\zIm}{Im} \newcommand{\conjug}[1]{\overline{#1}} % Calligraphic letters \newcommand{\sF}{\mathcal{F}} \newcommand{\sD}{\mathcal{D}} % Standard spaces \newcommand{\Hilb}{\mathcal{H}} \newcommand{\Le}{\mathbf{L}} % Operators and functions occassionally used in my articles \DeclareMathOperator{\D}{D} \DeclareMathOperator{\linspan}{span} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\lindim}{dim} \DeclareMathOperator{\sinc}{sinc} % Probability stuff \newcommand{\PP}{\mathbb{P}} \newcommand{\E}{\mathbb{E}}
<p> I hold a Bachelor's degree in pure mathematics and computer science, and a Master's degree in mathematical finance, both from the University of Toronto. </p> <p> I work at the front office on the trading floor in a major Canadian bank, implementing and testing models for valuating options and derivatives on equity (stock). In financial slang, a <i>quant</i> job. At the present time, my team is building a general computation engine for these models: techniques used include stochastic calculus, Monte Carlo simulation, PDEs (parabolic equations in particular) and Fourier transforms. </p> <p> Why do I write for PlanetMath? Not only for the love of mathematics, but also because I want to promote, in my own way, free culture and free software. And more practically, I find some topics, even elementary ones, that in my opinion are presented poorly or not properly in the textbooks that I own. So as I study those topics, I find myself making my own notes. Inevitably I type these up as the paper notes will become rather inconvenient in a few months' time. There is, of course, the usual argument that one learns by teaching; it does help me to understand a topic if try to write an exposition myself. </p> <p> By the way, if you want to read and write math formula in the forum posts in PlanetMath, consider using my <a href="">Display LaTeX</a> browser extension. (Mozilla-based browsers only.) </p> <p> Sources for the diagrams that I create on PlanetMath can be found in <a href="">my PlanetMath article repository</a>. Please feel free to re-use them! </p>