Welcome to Hanlon Financial Systems Lab

**"A Connection Between the Expansion of Filtrations and the Origin of Financial Bubbles"**

**BY: Philip Protter, Columbia University**

**Date & Time:** Tuesday, September 27, 2016, 4:30 pm

**Location:** Sherrerd Hall, room 101, Princeton University

**Abstract: **

Using the definition of a bubble as a strict local martingale, we show how under certain special circumstances a martingale can transform into a strict local martingale via an expansion of a filtration coupled with a change of the risk neutral measure. We then interpret this idea within the context of financial markets and the creation of bubbles, where a bubble can in theory be related to an influx of exciting information to the market. We give a mathematical construction of this can arise.

This talk is based on joint work with Aditi Dandapani.

**Bio: **

Professor Protter's primary research interests include mathematical finance (capital asset pricing theory, the pricing and hedging of derivatives, liquidity issues, financial bubbles, insider trading, high frequency trading, and credit risk), stochastic integration theory, stochastic differential equation theory, numerical solutions of stochastic differential equations, discretization of stochastic processes (as a branch of mathematical statistics), backward and forward-backwards stochastic differential equations, Markov process theory, and filtering theory. He has authored or co-authored two textbooks and two research books.

Professor Protter is a Fellow of the I.M.S., a Fellow of the A.A.A.S., and the Associate Editor of several research journals and is on two editorial boards, and is the former editor-in-chief of Stochastic Processes and their Applications. In 2007 he was a Fulbright Distinguished Chair at the University of Paris (Dauphine). He has been a visiting member of the Institute for Advanced Study, and he has been an invited visitor at many universities in the US and abroad. He has won two "best teacher" awards.