Stochastic Portfolio Theory Reading Seminar

Spring 2022


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

This Spring we we will continue 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 Mondays from 6p.m. to 7p.m. EDT.

This seminar is the continuation of the same seminar held in Fall - SPT Seminar, Fall 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
Monday, April 25, 6:00p.m. EDT Richard Groenewald The Kalman Filter and it's Applications in Parameter Estimation for Stochastic Volatility Models

Stochastic volatility models are a broad subset of the class of hidden Markov models in which the observable time series' variance is determined by another latent time series. We will overview the techniques involved in some of the practical approaches for parameter estimation in this setup, and discuss some applications to financial data.

Past Seminars

Date and time Speaker Title and abstract
Monday, January 31, 6:00p.m. EDT Richard Groenewald Continuing on Optimality Properties of the Supermartingale Numeraire

We will review some topics from the Fall semester since it has been a while and continue on where we left off, discussing the growth optimality, long run growth optimality and relative log optimality properties of the supermartingale numeraire.
Monday, February 7, 6:00p.m. EDT Richard Groenewald Some general local martingale properties and their application to "insider trading"

We prove some general results concerning strictly positive local martingales and discuss their application to the supermartingale numeraire in the context where an investor knows its all time minimum value.
Tuesday, February 15, 6:00p.m. EDT Richard Groenewald "Insider Trading" continued, a notion of robust long run growth, and stock only portfolios

We will finish last week's talk concerning insider trading and (time permitting) discuss the optimal long run growth rate when our stocks are Ito processes, and separately the notion of a local martingale numeraire portfolio which trades in stocks only.
Monday, February 21, 6:00p.m. EDT Sid Mane Optimal Execution Strategies for Portfolio Management

We have discussed Stochastic Portfolio Theory for the bulk of the last two semesters. Many times we have ignored the costs and risks that often characterize trade execution in public markets. In this talk, we zoom into exactly that gritty part of portfolio management. We turn our attention to another aspect of Portfolio Theory: optimal execution. Following a 2016 paper of Moallemi and Yuan, we will consider certain financial aspects of trading, use these to develop a model for transaction costs, and finally solve the associated optimal control problem. Along the way, we shall gain market intuition, observe an example of practical problem formulation in optimization, and obtain a healthy appreciation for convex functionals.
Monday, February 28, 6:00p.m. EDT Richard Groenewald Robust growth rate for markets of Ito diffusions and the stock portfolio local martingale numeraire

This talk will be split into two parts following pages 70 to 87 of Karatzas and Kardaras (2021): (1) we discuss the notion of a robust optimal long run growth rate when our stocks are Ito processes, and (2) necessary and sufficient conditions for the existence of a stock only local martingale numeraire portfolio, along with some of its properties.
Monday, March 7, 6:00p.m. EDT Georgy Gaitsgori Utility functions, risks and basic mean-variance analysis

We will introduce and discuss such notions as rational preferences, utility function, risk aversion, and measures of absolute risk aversion. We will then discuss basic mean-variance analysis and introduce a notion of the efficient frontier. Finally, if time permits we will discuss main results of the paper "Optimal basket liquidation for CARA investors is deterministic" by A. Schied, T. Schoneborn and M. Tehranchi, which state that sometimes determenistic liquidation strategies are as good as stochastic ones.
Monday, March 14, 6:00p.m. EDT No seminar (Spring break)

Monday, March 21, 6:00p.m. EDT Richard Groenewald The stock only local martingale numeraire

We cover the second part of the talk from February 28th: necessary and sufficient conditions for the existence of a stock only local martingale numeraire portfolio, along with some of its properties.
Monday, March 28, 6:00p.m. EDT No seminar

Monday, April 4, 6:00p.m. EDT Shalin Parekh Some results in weak KPZ universality

This is a practice talk for my defense. I'll talk about interacting particles, polymers, and convergence of these objects to an SPDE called the KPZ equation.
Monday, April 11, 6:00p.m. EDT No seminar

Monday, April 18, 6:00p.m. EDT Sid Mane Continuous-Time Methods in Contract Theory

After a brief introduction to incentive theory and contract design, we discuss Sannikov's model for a principal-agent problem in which the agent controls a drift-diffusion output. We will interpret the model dynamics, then derive and characterize the optimal contract for this environment.