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''Abstract:'' For the problem of portfolio optimization when returns and volatilities are driven by stochastic factors, approximations for value functions and optimal strategies have been proposed in the regime where these factors are running on slow and fast timescales. But, until now, rigorous results of accuracy of these approximations have only been obtained for cases that can be linearized, typically limited to power utilities and a single factor driving the environment. This talk is about treating cases with general utility functions and multi factors. Our approach is to construct sub- and super- solutions to the fully nonlinear problem such that their difference is at the desired level of accuracy. We first present a regular perturbation case with a power utility and two factors nearly fully correlated. Then, we show how to deal with a singular perturbation in the case of a general utility function with a fast varying factor. ''Abstract:'' For the problem of portfolio optimization when returns and volatilities are driven by stochastic factors, approximations for value functions and optimal strategies have been proposed in the regime where these factors are running on slow and fast timescales. But, until now, rigorous results of accuracy of these approximations have only been obtained for cases that can be linearized, typically limited to power utilities and a single factor driving the environment. This talk is about treating cases with general utility functions and multi factors. Our approach is to construct sub- and super- solutions to the fully nonlinear problem such that their difference is at the desired level of accuracy. We first present a regular perturbation case with a power utility and two factors nearly fully correlated. Then, we show how to deal with a singular perturbation in the case of a general utility function with a fast varying factor.
Joint work with Maxim Bichuch, Ruimeng Hu, and Ronnie Sircar. Joint work with Maxim Bichuch, Ruimeng Hu, and Ronnie Sircar.
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- 
''Moderator:'' [http://www.columbia.edu/~ac3827/ Agostino Capponi], Department of Industrial Engineering and Operations Research, Columbia University ''Moderator:'' [http://www.columbia.edu/~ac3827/ Agostino Capponi], Department of Industrial Engineering and Operations Research, Columbia University
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'''Thursday, September 17, 2020, 1PM-2PM''' (Eastern US; GMT-4); '''Thursday, September 17, 2020, 1PM-2PM''' (Eastern US; GMT-4);
-''Speaker:'' Rene Carmona, Professor of Engineering and Finance,ORFE and PACM, Princeton University+''Speaker:'' [https://carmona.princeton.edu/ Rene Carmona], ORFE and PACM, Princeton University

Revision as of 04:33, 20 July 2020

SIAG/FME virtual seminars series

The series of virtual talks, started by the SIAM Activity Group on Financial Mathematics and Engineering (SIAG/FME), aims at keeping the mathematical finance community connected worldwide beyond traditional formats. The goal is to host a diverse, across all dimensions, lineup of prominent speakers that will present the latest developments in the area of financial mathematics and engineering.

\diamond The talks will run every other week, and at least until the next SIAG/FME Biennial Meeting in June 2021

\diamond The talks will alternate with those set up by the Bachelier Finance Society

\diamond All talks will be delivered remotely using Zoom.

\diamond The talks are open to the public. Due to security reasons, all attendees have to register.

\diamond The registration link will be posted on this web-site, next to the each seminar date below. The detailed information about each talk, and the registration link will be also distributed via SIAG/FME Mailing List.

\diamond The registration is quick (asks only for your name and email), and once registered, you will receive an email with the link to the meeting(s), which is unique to you, so please do not share that email. The registration is usually valid for multiple future talks.


SIAG/FME Seminar Series Committee:

\quad Agostino Capponi (SIAG/FME Chair, Columbia University)

\quad Igor Cialenco (SIAG/FME Program Director, Illinois Institute of Technology)

\quad Sebastian Jaimungal (University of Toronto)

\quad Ronnie Sircar (Princeton University)


Forthcoming Talks



Thursday, June 25, 2020, 1PM-2PM (Eastern US; GMT-4); Registration Link

Speaker: Jean-Pierre Fouque, University of California Santa Barbara

Image:JP1.jpg

Title: Accuracy of Approximation for Portfolio Optimization under Multiscale Stochastic Environment

Abstract: For the problem of portfolio optimization when returns and volatilities are driven by stochastic factors, approximations for value functions and optimal strategies have been proposed in the regime where these factors are running on slow and fast timescales. But, until now, rigorous results of accuracy of these approximations have only been obtained for cases that can be linearized, typically limited to power utilities and a single factor driving the environment. This talk is about treating cases with general utility functions and multi factors. Our approach is to construct sub- and super- solutions to the fully nonlinear problem such that their difference is at the desired level of accuracy. We first present a regular perturbation case with a power utility and two factors nearly fully correlated. Then, we show how to deal with a singular perturbation in the case of a general utility function with a fast varying factor. Joint work with Maxim Bichuch, Ruimeng Hu, and Ronnie Sircar.

Moderator: Agostino Capponi, Department of Industrial Engineering and Operations Research, Columbia University


Thursday, July 09, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:


Thursday, July 23, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:



Thursday, August 06, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:



Thursday, August 20, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:


Thursday, September 3, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:



Thursday, September 17, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker: Rene Carmona, ORFE and PACM, Princeton University


Title: TBA

Abstract: TBA

Moderator:



Thursday, October 1, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:


Thursday, October 15, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:


Thursday, October 29, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker:

Title: TBA

Abstract: TBA

Moderator:


.

Past Talks




Thursday, June 11, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker: Patrick Cheridito, ETH Zurich

Image:Patrick1.jpg

Title: Deep optimal stopping

Abstract: I present a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can efficiently be simulated. The approach is tested on three problems: the pricing of a Bermudan max-call option, the pricing of a callable multi barrier reverse convertible and the problem of optimally stopping a fractional Brownian motion. In all three cases it produces very accurate results in high-dimensional situations with short computing times. Joint work with Sebastian Becker and Arnulf Jentzen.

Moderator: Sebastian Jaimungal, Department of Statistical Sciences, University of Toronto



Thursday, May 28, 2020, 1PM-2PM (Eastern US; GMT-4);

Panel Discussion: Energy Markets

Recorded Video

Abstract: The aim is to discuss recent events in energy/electricity/commodity markets, such as negative prices, as well as related mathematical modeling challenges.

Panelists:

Image:ReneAid1.jpg \qquad Rene Aid, Université Paris-Dauphine, France

Image:swindle1.jpg \qquad Glen Swindle, Scoville Risk Partners, USA

Image:Zef1.jpg \qquad Zef Lokhandwalla, Bloomberg LP, USA

Image:Mike1.jpg \qquad Mike Ludkovski, University of California Santa Barbara, USA

Moderator: Ronnie Sircar, ORFE, Princeton University



Thursday, May 14, 2020, 1PM-2:30PM (Eastern US; GMT-4);

Speaker: Bruno Dupire, Head of Quantitative Research, Bloomberg LP

Image:Bruno1.jpg

Title: The Geometry of Money and the Perils of Parameterization

Recorded Video

Abstract: Market participants use parametric forms to make sure prices are orderly aligned. It may prevent static arbitrages but could it lead to dynamic arbitrages? Markets trade thousands of underlying, each one with tens or even hundreds of options, quoted throughout the day. Needless to say, the quotes are not generated manually. They are automated and derived from a functional form with a few parameters. If we know this parameterization, we know in advance how the prices tomorrow of many traded securities will belong to a low dimensional (number of parameters) manifold in a high dimensional (number of securities). If the vector of today prices does not belong to the convex hull of the manifold it creates arbitrage. We examine market practice (Black-Scholes, stochastic volatility models, interest rate interpolation by piecewise constant instantaneous forward rates, converging implied volatilities for extreme strikes in FX...) and show that many violate the no arbitrage condition.

Moderator: Igor Cialenco, Illinois Institute of Technology



Thursday, April 30, 2020, 1PM-2PM (Eastern US; GMT-4);

Speaker: Blanka Horvath, Department of Mathematics, King's College London, UK

Image:Horvath1.jpg


Title: A Data-driven Market Simulator for Small Data Environments

Recorded Video

Abstract: In this talk we investigate how Deep Hedging brings a new impetus into the modelling of financial markets. While a DNN-based data-driven market generation unveils a new and highly flexible way of modelling financial time series, it is by no means "model-free". In fact, the concrete modelling choice is decisive for the features of the resulting generative model. After a very short walk through historical market models we proceed to neural network based generative modelling approaches for financial time series. We then investigate some of the challenges to achieve good results in the latter, and highlight some applications and pitfalls. While most generative models tend to rely on large amounts of training data, we present here a parsimonious generative model that works reliably even in environments where the amount of available training data is notoriously small. Furthermore, we discuss how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series data in such environments. Lastly, we also discuss some pricing and hedging considerations in a DNN framework and their connection to Market Generation. The talk is based on joint work with H. Buehler, I. Perez Arribaz, T. Lyons and B. Wood.

Moderator: Agostino Capponi, Department of Industrial Engineering and Operations Research, Columbia University



Thursday, April 16, 2020, 1PM-2PM (Eastern US; GMT-4)

Speaker: Mete Soner, Department of Operations Research and Financial Engineering, Princeton University

Image:soner.jpg

Title: Trading with impact

Recorded Video

Abstract: It is well known that large trades cause unfavorable price impact resulting in trading losses. These losses are particularly high when the underlying instrument is not liquid enough or when the trade size is large. Other type of market frictions such as transaction costs also cause similar effects. When one considers hedging or portfolio management or equilibrium models these effects must be taken into account. After describing widely used approaches of Cetin, Jarrow & Protter and Almgren & Chris, I first study the impact of resilience and then the structure of the optimal portfolios. This talk will be a summary of many results obtained jointly with many people including, Peter Bank, Bruno Bouchard, Umut Cetin, Ludovic Moreau, Johannes Muhle-Karbe, Nizar Touzi and Moritz Voss.

Moderator: Sebastian Jaimungal, Department of Statistical Sciences, University of Toronto

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