Stochastic Portfolio Theory Reading Seminar

Fall 2021


Welcome to the Stochastic Portfolio Theory Reading Seminar, run by the students of Columbia University.

This Fall we we will be studying Portfolio Theory and Arbitrage: A Course in Mathematical Finance by I. Karatzas and C. Kardaras. Our talks will be held in hybrid form over Zoom and in Columbia University on Fridays from 4p.m. to 5p.m. EDT.

This seminar is the continuation of the same seminar held in Summer - SPT Seminar, Summer 2021.

If you would like to come to our seminars or to be added on the mailing list, please email ggaitsgori@math.columbia.edu.

Next Seminar

Date and time Speaker Title and abstract
Friday, October 15, 4:00p.m. EDT Georgy Gaitsgori Stochastic Portfolio Theory - New and old definitions (PTA, Chapter 1)

We start discussing the book "Portfolio Theory and Arbitrage" by I.Karatzas and C.Kardaras. In particular, we will try to cover Chapter 1 of this book. We will revisit old definitions of stock prices, portfolios and functionally generated portfolios. We will also generalize these notions and introduce new notions of wealth process, numeraire, and others.

Past Seminars

Date and time Speaker Title and abstract
Friday, October 1, 4:00p.m. EDT Richard Groenewald Functionally Generated Trading Strategies in Markets of General Continuous Semimartingales

We discuss generalizing the approach taken in Fernholz's Stochastic Portfolio Theory text to markets whose stock price processes are arbitrary continuous semimartingales, and outline an alternative "additive" portfolio generation. We will also introduce sufficient conditions for both long and short-term arbitrage with respect to the market portfolio, and review some specific examples.
Friday, October 8, 4:00p.m. EDT Richard Groenewald Arbitrage and a New Class of Portfolio Generating Functions

We continue to discuss sufficient conditions for both long and short term arbitrage with respect to the market portfolio in markets whose stock price processes are general continuous semimartingales. We will also develop some notions of portfolio generating functions which take inputs other than the market weights alone.