Category: Mathematics
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Algorithmic Trading by EP Chan (Notes Part 1)
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in MathematicsThis post summarizes some notes that I took from the book “Algorithmic Trading” by Ernest Chan. I’m already familiar with some concepts, so these notes only cover the new concepts I learned. I strongly recommend that you buy the book (it’s a good book) for more details and information. Chapter 1: Backtesting and Automated Execution…
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The Lagrange Method for Optimization
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in MathematicsThe Lagrange method can be used to help us perform optimization by determining the relative weightage of each asset in order to minimize portfolio variance or maximize returns. First, we need to form a Lagrangian function L(x, λ) augmented by the addition of the constraint functions. Each constraint function is multiplied by a variable, called…
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Different Forms of Itô’s Lemma
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in MathematicsCase 1: Function is in terms of X (Brownian Motion) Case 1a: F = F(X) Case 1b: F = F(t, X) Case 2: Function is in terms of Z Case 2a: F = F(Z) Case 2b: F = F(t, Z)
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Solving 2nd Order ODE
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in MathematicsCase 1: Homogeneous Case 1a Case 1b Case 1c Case 2: Non Homogeneous To find yp, we make an educated guess using the method of undetermined coefficients. This works if d(x) is: Polynomial Exponential (i.e. Aekx, provided k is not a root of ay” + by’ + c = 0) Trigonometry (i.e. Asinkx + Bcoskx,…
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Solving 1st Order ODE
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in MathematicsCase 1: x missing Example: Case 2: y missing Case 3: Variable Separable Example: Case 4: Linear Equations Verification:
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Pre-Calculus – Trigonometry and Vectors
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in MathematicsThese are some notes that I took from a pre-calculus course. I wish I have time to type these notes out…
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Itô’s Integral
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in MathematicsThis post is on Itô’s Integral. The notes are taken from the second part of the MIT OpenCourseWare lecture linked in the previous post on Ito’s lemma. I’m kind of lost when he discussed Itô Isometry. Did more research for a better understanding. The first video below gives a more concrete explanation of Itô’s integral.…
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Itô’s Lemma Examples
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in MathematicsNotes taken from the first half of the Itô’s Calculus lecture by MIT OpenCourseWare.
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Brownian Motion 2
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in MathematicsThis is just another post that discusses the Brownian Motion (based on the MIT OpenCourseWare lecture embedded below).