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Taylor Martin
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### Taylor Martin

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A Primer in Harmonic Analysis
I picked these problems from Modern Fourier Analysis Vol I - I think that they serve as a good primer for the basic techniques and theorems in harmonic analysis (a subject that I have recently started looking back into in order to deal with some of the tech...﻿
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### Taylor Martin

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Does the Trigonometric Harmonic Series Converge?
It is well known that the harmonic series $H(x)=\sum_{n=1}^{\infty} xn^{-1}=+\infty$ for every $x\neq=0$, but what about the trigonometric harmonic series $T(x)=\sum_{n=1}^{\infty}e^{inx}n^{-1}$?

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### Taylor Martin

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The Black-Scholes Model
In this post we take the PDE approach to pricing derivatives in the Black-Scholes universe.  In a subsequent approach we will cover the risk-neutral valuation approach; the two are essentially equivalent by the  Feynman-Kac formula . I. ASSUMPTIONS We will ...﻿
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### Taylor Martin

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Analysis of the Black Scholes PDE
In this post we conduct a cursory analysis of the Black-Scholes (B-S) partial differential equation (PDE), including existence and uniqueness of solutions, well-posedness, and in certain special circumstances, analytical solutions. The B-S PDE is defined th...﻿
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