This event is a one-day workshop on Stochastic Portfolio Theory (SPT). SPT is a mathematical framework to study large equity markets that was introduced by Robert Fernholz in 2002. The goal of the workshop is to bring together leading researchers in the area to discuss the field, as well as recent developments and trends.

Registration is required. If you are interested in attending please inquire with the organizer at d.itkin@imperial.ac.uk. Complimentary lunch and coffee will be provided to all attendees.

Schedule

Titles/Abstracts

Professor Ioannis Karatzas: 

Title: VOLATILITY AND ARBITRAGE

Abstract: Can the market portfolio be outperformed? If not, why? If yes, under what conditions? over which time-horizons? by what portfolios? and can said conditions and portfolios be described in terms only of observables, without resorting to any model assumptions? Questions such as these lead to some pretty interesting mathematics, both in probability theory and in differential geometry. We shall discuss some results in this vein, and suggest open problems. (Joint work with E.R. Fernholz and J. Ruf.)

Professor Johannes Ruf

Title: Short- and long-term relative arbitrage in stochastic portfolio theory

Abstract: A basic result in Stochastic Portfolio Theory states that a mild nondegeneracy condition suffices to guarantee long-term relative arbitrage, that is, the possibility to outperform the market over sufficiently long time horizons. A longstanding open question has been whether short-term relative arbitrage is also implied. Fernholz, Karatzas & Ruf recently showed that it is not, without giving tight bounds on the critical time horizon. We connect existence of relative arbitrage to a certain geometric PDE describing mean curvature flow, and use properties of such flows to compute the critical time horizon. Joint work with Martin Larsson

Professor Kostas Kardaras

Title: Portfolio choice under taxation and expected market time constraint

Abstract: We consider the problem of choosing an investment strategy that will maximise utility over distributions, under capital gains tax and constraints on the expected liquidation date. We show that the problem can be decomposed in two separate ones. The first involves choosing an optimal target distribution, while the second involves optimally realising this distribution via an investment strategy and stopping time. For the latter step, a variant of the Azema-Yor solution to the Skorokhod embedding problem is utilised, and its description is given very precisely in terms of the first time that the wealth of the growth optimal portfolio, properly taxed, crosses a moving stochastic (depending on its infimum) level of its maximum.

Dr. David Itkin

Title: Ergodic Robust Maximization of Asymptotic Growth under Stochastic Volatility

Abstract: We consider an asymptotic robust growth problem under model uncertainty and in the presence of (non-Markovian) stochastic covariance. Building on the previous work of Kardaras & Robertson we fix two inputs representing the instantaneous covariation and invariant density for the asset process X, but additionally allow these quantities to depend on a stochastic factor process Y. Under mild technical assumptions we are able to show that the robust growth optimal strategy is functionally generated and, unexpectedly, does not depend on the factor process Y. We present two financial interpretations for this result and consider some examples. The technical tools used to establish the main result rely on a combination of PDE and generalized Dirichlet form techniques. This talk is based on joint work with Benedikt Koch, Martin Larsson and Josef Teichmann.