Below, you'll find a random collection of my notes on probability theory, mathematics, and finance.  If you download these notes, please be aware of the following:
  • These notes were written as I was first learning this material.  As such, the notes almost surely (i.e. with probability one) contain errors.  If (meaning "when") you find errors in my notes, I would greatly appreciate it if you would tell me.  That way, I can correct the errors so that others trying to learn this material do not need to sort through them.
  • The "proofs" in my notes are intended to be heuristic -- not rigorous.  Mathematical rigor was sacrificed in order that the reader can gain an intuitive understanding of the underlying concepts.
Despite the above shortcoming, I hope that, by posting these notes, you can learn something from them.  Topics covered below (listed in no particular order) include:
  • ***NEW*** Spectral Decomposition of 1-D Diffusions
  • Fourier Transforms and Green's Functions
  • Probabilistic Solutions to Boundary Value Problems
  • Discrete-Time Martingales
  • Sigma Algebras
  • The connection between Stochastic Differential Equations and Partial Differential Equations (Feynman-Kac Formula, Kolmogorov Forward and Backward Equations)
  • Local Volatility
  • Heston's Stochastic Volatility
  • Sturm-Liouville Theory
  • Heat Equation
  • Girsanov Change of Measure
  • Absorbing vs Reflecting Boundary Conditions
Enjoy!

SpectralDecompositionDiffusion1.00.pdf SpectralDecompositionDiffusion1.00.pdf
Size : 152.741 Kb
Type : pdf
Fourier Xforms and Greens Funcs.pdf Fourier Xforms and Greens Funcs.pdf
Size : 0.027 Kb
Type : pdf
Boundary Value Problems.pdf Boundary Value Problems.pdf
Size : 0.042 Kb
Type : pdf
DiscreteMartingaleNotes.pdf DiscreteMartingaleNotes.pdf
Size : 0.081 Kb
Type : pdf
sigma algebras.pdf sigma algebras.pdf
Size : 0.049 Kb
Type : pdf
SDE PDE connection notes.pdf SDE PDE connection notes.pdf
Size : 0.167 Kb
Type : pdf
Local Volatility.pdf Local Volatility.pdf
Size : 0.063 Kb
Type : pdf
HestonStochasticVolatility4.pdf HestonStochasticVolatility4.pdf
Size : 0.086 Kb
Type : pdf
SturmLiouville.pdf SturmLiouville.pdf
Size : 0.051 Kb
Type : pdf
HeatEqnMixedDerivatives.pdf HeatEqnMixedDerivatives.pdf
Size : 0.284 Kb
Type : pdf
Girsanov2.pdf Girsanov2.pdf
Size : 0.036 Kb
Type : pdf
AbsorbingVsReflectingBoundaries.pdf AbsorbingVsReflectingBoundaries.pdf
Size : 0.063 Kb
Type : pdf

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