Mathematical Option Pricing. Course Material and Supplementary Pieces 1

A pike from the Medway, my daughter holds the fish. It was just under
      20lbs in weight


This pike weighed a little under 20lbs and was caught on a sprat just downstream of Teston Bridge during the spring of 2008. My daughter, Edele, holds the fish.

The files which appear first below are concerned with background material for Mathematical Finance. It includes some integration theory and some important (but tedious?) material about Stochastic Processes.

The files, "Families of Sigma Fields" give an introduction to Conditional Expectation and Stochastics Bases.

Notes on Condex , Part 1 of the notes on sigma fields , Part 2 of the notes on sigma fields, Part 3 of the notes on sigma fields.

This file summarizes integration theory used in Probability. Thanks are due to Chris Ridler-Rowe for this summary.

This file gives a first course in Abstract Integration. It is modelled on Walter Rudin's (excellent) treatment.

This file takes the discussion of Measurable Functions a little further.

This file looks at the conditional expectation on $L^{1}$. Conditional Expectation

The files Doob_Meyer_1 and Doob_Meyer_2 give a treatment of the Doob_Meyer Decomposition for a submartingale. Along the way the idea of a Natural process is introduced. In discrete time, Natural is equivalent to Predictable in the strongest sense. In continuous time you modify your idea of equivalent for the result to remain true.

Notes on the Hahn-Banach Theorem

  • Mathematical Option Pricing. Supplementary Material 2
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  • Problems (and solutions) for Stochastic Processes I.
  • Resources for Research Students in Mathematical Finance.
  • Research Interests
  • Lebesgue Integration

  • Chris Barnett
    Department of Mathematics
    Imperial College
    London SW7 2AZ
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