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The Thalesians

Some of our talks

Images from Thalesians events from around the world over the past 6 years

The Thalesians are a think tank of dedicated professionals with an interest in quantitative finance, economics, mathematics, physics and computer science, not necessarily in that order.

Blog / See our new Thalesians blog / Book / Buy our new book, Trading Thalesians - What the ancient world can teach us about trading today (Palgrave Macmillan) by the Thalesians co-founder, Saeed Amen & foreword by founder, Paul Bilokon

Founding / The group was founded in Sep 2008, by Paul Bilokon (then a quantitative analyst at Lehman Brothers specialising in foreign exchange, and a part-time researcher at Imperial College), and two of his friends and colleagues: Matthew Dixon (then a quantitative analyst at Deutsche Bank) and Saeed Amen (then a quantitative strategist at Lehman Brothers).

Events / Research / Consulting

Events / The Thalesians were originally based in London, UK. In Jan 2011, the organisation became truly global when Matthew Dixon brought it to the United States where he runs the Thalesians NYC seminars with New York Leader Harvey Stein. Attila Agod is the Budapest Leader for our Thalesians Budapest seminars. We are currently in the process of expanding our seminars to Prague and running more workshops.

Research / In late 2013, we started published ground breaking quant strategy notes. Our effort is lead by Saeed Amen, using nearly a decade of his experience both creating and later trading systematic trading models in FX at major investment banks. Visit Research for more.

Consulting / In 2014, we started offering bespoke quant consulting services in markets, signing up our first client, a major US hedge fund and RavenPack, a major news data vendor. Our services includes the creation of bespoke systematic trading models and other quant analysis of financial markets, such as currency hedging and FX transaction cost analysis (TCA). Visit Consulting for more.

Timeline

Our Philosophy

We are named after Thales of Miletus (Θαλῆς ὁ Μιλήσιος), a pre-Socratic Greek philosopher who lived in ca. 624 BC-ca. 546 BC. Thales was a mathematician and is familiar to many secondary school students for one of his theorems in geometry.

But more relevantly to us, he was one of the first users of options:

"Thales, so the story goes, because of his poverty was taunted with the uselessness of philosophy; but from his knowledge of astronomy he had observed while it was still winter that there was going to be a large crop of olives, so he raised a small sum of money and paid round deposits for the whole of the olive-presses in Miletus and Chios, which he hired at a low rent as nobody was running him up; and when the season arrived, there was a sudden demand for a number of presses at the same time, and by letting them out on what terms he liked he realised a large sum of money, so proving that it is easy for philosophers to be rich if they choose, but this is not what they care about."Aristotle, Politics, 1259a.

The morale of this anecdote is that it is easy for philosophers to be rich if they choose; the famous Milesian went ahead and proved it.

We, the Thalesians, admire him for that. But we also share many of his values, for example his core belief that a happy man is defined as one "ὁ τὸ μὲν σῶμα ὑγιής, τὴν δὲ ψυχὴν εὔπορος, τὴν δὲ φύσιν εὐπαίδευτος" (who is healthy in body, resourceful in soul and of a readily teachable nature).

This wiki was created to serve as a source of information on quantitative finance, to collate references to various related resources, and to serve as a convergence point for the Thalesians, our colleagues and collaborators. It grew out of Paul Bilokon's finance wiki, which he started in February, 2007.

We believe that secrecy and fidelity are important in the world of finance. But we also acknowledge the power of information sharing in open societies. Let your business logic remain a closely guarded secret. But release everything else into the public domain. What goes around, comes around; this will ultimately spare you reinventing the wheel.

Some of our talks

More of our speakers at Thalesians events over the past 6 years


Forthcoming Events

Global Derivatives Europe (Amsterdam - External Event) — Speakers including Hull — Trading and risk management

Saeed Amen

Saeed Amen

Date and Time

18th - 22nd May, 2015

Venue

Hotel Okura, Amsterdam, The Netherlands.

To sign up

You can register for this event and pay online at the Global Derivatives Europe website: http://www.icbi-derivatives.com/FKN2428THW

Members of the Thalesians also have a special 10% discount (please contact saeed who happens to be at thalesians.com for details - clicking the link above will also activate this discount)

Abstract

The World's Leading Quantitative Finance Conference: Cutting Edge Strategies & Practical Techniques For Advanced Derivatives Pricing, Hedging, Trading & Risk Management

Global Derivatives brings together leading quants, traders, risk managers and academics from all over the world to discuss the key challenges affecting the derivatives market. Attending will enable you to:

  • Hear technical details of the latest research being done by leading financial minds
  • Learn cutting edge volatility, correlation, interest rate, FX, equities & credit modelling techniques
  • Discover practical solutions to the challenges you face & learn how to implement them when you get back in the office
  • Meet and learn from hundreds of senior derivatives professionals

What Topics Will Be Covered At Global Derivatives Trading & Risk Management 2015?

  • Now in its 22nd year, Global Derivatives brings together senior practitioners from banks, asset managers, hedge funds, pension funds, propr trading firms, private equity firms, exchanges as well as academics and regulators to discuss the key issues facing quants all over the world.

The event will address topics in 4 key areas:

  • Derivatives Pricing
  • Regulation, Risk Management & Capital Optimisation
  • Quantitative Investment Strategies & Portfolio Optimisation
  • Algorithmic Trading

Speaker

Speakers include many well known figures from the finance community, such as Riccardo Rebonato, John Hull, Darrell Duffie and Emanuel Derman. Saeed Amen, a co-founder of the Thalesians is also speaking on FX vol & Big Data trading strategies.


Thalesians Seminar (London) — Artur Sepp — Gaining the alpha advantage in vol trading

Artur Sepp

Artur Sepp

Date and Time

7:30 p.m. on Wednesday, 27 May, 2015

Venue

Ginger Room, Marriott Hotel, Canary Wharf, London, UK.

Meetup.com

You can register for this event and pay online on Meetup.com: http://www.meetup.com/thalesians/events/222379514/

Abstract

We start by presenting some empirical evidence for short volatility strategies and the cyclical pattern of their P&L resulting in alpha in good times but beta in bad times.

We relate the risk-premium observed in volatility strategies as a compensation to bear losses in bad market regimes. While in normal market regimes the positive risk-premium contributes to the positive expected P&L for volatility strategies, large negative spikes in the risk-premium lead to sharp losses for vol strategies during bad market regimes. The million-dollar question is how to manage vol strategies with respect to market cycles?

First, we introduce a factor model to explain the risk-premium using the risk-aversion of investors and heavy-tails of returns distributions under the statistical measure.

Second, we consider an econometric model for statistical inference of market regimes and for optimal position sizing with respect to forecast probabilities of regimes.

Finally, we illustrate model applications for generating alpha from volatility strategies.

Speaker

Artur Sepp works for Global Risk Analytics at Bank of America Merrill Lynch focusing on firm-wide risk-return optimization. Prior to that, he worked as equity and credit derivatives quant at Merrill Lynch and Bear Stearns with particular emphasis on credit and volatility modelling and trading. Artur has a PhD in Probability and Statistics from the University of Tartu in Estonia, an MSc in Industrial Engineering from Northwestern University in Chicago, and a BA in Mathematical Economics. His research area is on volatility models, computational methods, investment and trading strategies. Artur has published several research articles on quantitative finance in leading journals and he serves as an associate editor for the Journal of Computational Finance.


Thalesians Seminar (Prague) — Saeed Amen — Trading Thalesians book talk / Python FX intraday demo

Saeed Amen

Saeed Amen

Date and Time

7:00 p.m. on Friday, 29 May, 2015

Venue

Konferenční sály Akademie věd ČR, Národní 1009, Praha 1, Czech Republic

Meetup.com

You can register for this FREE event at Meetup.com: http://www.meetup.com/thalesians/events/222183063/

Abstract

Thanks to Jan Novotny and Pavel Motuzenko for helping to organise our first Thalesians talk in Prague!

First half: What can the ancient world teach us about modern money markets? How can we use examples from the ancient world, philosophers and writers to better understand the markets? Just as historians such as Herodotus living in ancient Greece examined the past, can traders look to their past to learn something new? In this exciting new book, Saeed Amen looks to the ancient world to help us better understand modern money markets, demonstrating what ancient philosophers can teach us about trading markets today, and showing readers how to maximize their returns.

Second half: We leap into modern day, we will use Python in an interactive demo to investigate the properties of FX intraday price action and volatility, using FX tick data, in particular noting various patterns in price action. We shall also be discussing FX intraday price dynamics around ECB meetings.

Copies of Trading Thalesians will be available at the end of the talk, personally signed by the author!

Speaker

Saeed Amen is a Managing Director and a Co-founder at Thalesians Ltd.

Saeed is currently publishing ground-breaking quant strategy notes at Thalesians Ltd., drawing upon nearly a decade of experience both creating and running systematic trading models successfully with real cash. Independently, he is also a systematic FX trader, running a proprietary trading book trading liquid G10 FX. He is currently also writing a book on trading which is due to be published by Palgrave Macmillan (preliminary title: Trading Thalesians - What the ancient world can teach us about trading today)

Saeed started his career at Lehman Brothers. He worked on the FX desk developing systematic trading models for both G10 and EM and was part of the team who developed the MarQCuS suite of models. He was also responsible for a systematic FX prop trading book and conducted research around high frequency FX including economic events. Later he was at Nomura as an Executive Director in Quantitative Strategy, also in FX, developing their model infrastructure and also running systematic FX prop risk. He graduated from Imperial College with a first class honours master's degree in Mathematics and Computer Science.


Thalesians Seminar (Frankfurt) — Saeed Amen — Trading Thalesians book talk / Python FX intraday demo

Saeed Amen

Saeed Amen

Date and Time

6:00 p.m. on Wednesday, 3 June, 2015

Venue

Die-Zentrale, Berger Strasse 175, Frankfurt am Main, Germany

Meetup.com

You can register for this event and pay online on Meetup.com: http://www.meetup.com/thalesians/events/222182763/

Abstract

First half: What can the ancient world teach us about modern money markets? How can we use examples from the ancient world, philosophers and writers to better understand the markets? Just as historians such as Herodotus living in ancient Greece examined the past, can traders look to their past to learn something new? In this exciting new book, Saeed Amen looks to the ancient world to help us better understand modern money markets, demonstrating what ancient philosophers can teach us about trading markets today, and showing readers how to maximize their returns.

Second half: We leap into modern day, we will use Python in an interactive demo to investigate the properties of FX intraday price action and volatility, using FX tick data, in particular noting various patterns in price action. We shall also be discussing FX intraday price dynamics around ECB meetings.

Copies of Trading Thalesians will be available at the end of the talk, personally signed by the author!

Selected Bios

Saeed Amen is a Managing Director and a Co-founder at Thalesians Ltd.

Saeed is currently publishing ground-breaking quant strategy notes at Thalesians Ltd., drawing upon nearly a decade of experience both creating and running systematic trading models successfully with real cash. Independently, he is also a systematic FX trader, running a proprietary trading book trading liquid G10 FX. He is currently also writing a book on trading which is due to be published by Palgrave Macmillan (preliminary title: Trading Thalesians - What the ancient world can teach us about trading today)

Saeed started his career at Lehman Brothers. He worked on the FX desk developing systematic trading models for both G10 and EM and was part of the team who developed the MarQCuS suite of models. He was also responsible for a systematic FX prop trading book and conducted research around high frequency FX including economic events. Later he was at Nomura as an Executive Director in Quantitative Strategy, also in FX, developing their model infrastructure and also running systematic FX prop risk. He graduated from Imperial College with a first class honours master's degree in Mathematics and Computer Science.


2nd Big Data Quant Finance Conference (London - External Event) — Speakers including Albanese and Amen

Claudio Albanese

Claudio Albanese

Date and Time

10th-12th June 2015

Venue

London

To sign up

You can register for this event and pay online at the WBS Training website: http://www.wbstraining.com/php/conferences/?id=103 (contact saeed at thalesians.com for a 25% discount code, which is available for Thalesians members!)

Abstract

This conference will showcase some of the latest progress made in financial data:

  • Deutsche Börse: Big Data Enabling Technologies – A Financial Market Perspective
  • Bloomberg will explore Newscasting - Forecasting Global Macro Economic Data from News and Events
  • UBS discuss High-Frequency Beta Estimation in Practice
  • ABN AMRO Analyze Large Volume Transactions on Capital Markets
  • Natixis will present Anomaly Detection in Sensitivity Computation by Machine Learning Techniques
  • Global Valuation Limited present on the latest develoements on Capital Simulations for OTC books
  • RavenPack open the conference with Tales from the Front Line; The Quant Market for Big Data
  • The Python Quants look at How Open Source Revolutionizes Financial Analytics

Speaker

  • Maurizio Luisi: Senior Quantitative Strategist, Bloomberg LP
  • Dragos Crintea: External IT Consultant, Deutsche Börse
  • Tobias Preis: Associate Professor of Behavioural Science and Finance, Warwick Business School, University of Warwick
  • David Jessop: Managing Director – Global Head of Equities Quantitative Research, UBS
  • Jose Luu: Head of Scientific Computing, Natixis
  • Yves J. Hilpisch: The Python Quants
  • Igor Stojkovic: Business Advisor Big Data Scientist, ABN Amro
  • Hugh Taggart: Director of Business Development, RavenPack
  • Claudio Albanese: CEO: Global Valuation Limited
  • Saeed Amen: Managing Director & Co-founder: THE THALESIANS
  • Bas van Schriek: Risk Manager: ABN Amro
  • Other presenters to be confirmed

Pre-Conference Workshop Day: Wednesday 10th June: Exploring Themes in Systematic Trading by Saeed Amen: Managing Director & Co-founder: THE THALESIANS


Thalesians Seminar (London) — AHL — Using Python to build trading strategies with AHL

AHL

Man AHL

Date and Time

7:00 p.m. on Wednesday, 17 June, 2015

Venue

AHL, Riverbank House, 2 Swan Lane, London EC4R 3AD

Meetup.com

You can register for this FREE event on Meetup.com: http://www.meetup.com/thalesians/events/222320925/

Abstract

FREE evening of talks, kindly hosted by AHL at their London headquarters

The AHL team will be discussing how they use their Python based research platform to research quantitative trading systems. There will also be a real life Python demo, illustrating how they use it in practice.

There will also be a demo from Saeed Amen (from Thalesians), showing how to use Python to investigate the properties of intraday FX volatility, where he'll be accessing live market data via Bloomberg and also creating customised plots using Matplotlib.

Selected Bios

Saeed Amen is a Managing Director and a Co-founder at Thalesians Ltd.

Saeed is currently publishing ground-breaking quant strategy notes at Thalesians Ltd., drawing upon nearly a decade of experience both creating and running systematic trading models successfully with real cash. Independently, he is also a systematic FX trader, running a proprietary trading book trading liquid G10 FX. He is currently also writing a book on trading which is due to be published by Palgrave Macmillan (preliminary title: Trading Thalesians - What the ancient world can teach us about trading today)

Saeed started his career at Lehman Brothers. He worked on the FX desk developing systematic trading models for both G10 and EM and was part of the team who developed the MarQCuS suite of models. He was also responsible for a systematic FX prop trading book and conducted research around high frequency FX including economic events. Later he was at Nomura as an Executive Director in Quantitative Strategy, also in FX, developing their model infrastructure and also running systematic FX prop risk. He graduated from Imperial College with a first class honours master's degree in Mathematics and Computer Science.


IAQF-Thalesians Seminar (New York) — Dr. Tim Leung — Exchange-Traded Funds and Related Trading Strategies

Tim Leung

Tim Leung

Agenda

Wednesday, June 18, 2015:

Venue

NYU Kimmel Center, Room 914, Kimmel Center, 60 Washington Square South, NY 10012, NY

Registration

Abstract

We discuss a number of static and dynamic portfolios related to exchange-traded funds (ETFs). We first discuss the price dynamics of futures-based ETFs and leveraged ETFs. This leads us to develop futures-based strategies for the objective of leverage replication, and discuss their applications to VIX and commodity (L)ETFs. We also analyzed several trading strategies involving multiple leveraged ETFs, accounting for their leverage ratios, volatility decays, expense ratios, and tracking errors. The performance and risk characteristics of these portfolios are studied both analytically and empirically.

Speaker

Tim Leung is an Assistant Professor at Columbia University's IEOR Department. He's also an affiliated faculty member of the Center for Financial Engineering, and Institute for Data Sciences & Engineering. He received a Ph.D. in Operations Research & Financial Engineering (ORFE) from Princeton University, and B.S. in Operations Research & Industrial Engineering (ORIE) at Cornell University.

Professor Leung's research focuses on the valuation of financial derivatives, and associated risk management and trading strategies. In particular, he has written extensively on exchange-traded funds (ETFs). His research has been funded by the National Science Foundation (NSF), and published in journals, such as Mathematical Finance, Finance & Stochastics, Quantitative Finance, and SIAM Journals.

IAQF-Thalesians Seminars

The IAQF-Thalesians Seminar Series is a joint effort on the part of the IAQF (formerly IAFE) and the Thalesians. The goal of the series is to provide a forum for the exchange of new ideas and results related to the field of quantitative finance. This goal is accomplished by hosting seminars where leading practitioners and academics present new work, and following the seminars with a reception to facilitate further interaction and discussion. The seminar series is limited to IAQF and Thalesians members only.


The 1st Central & Eastern European Quant Finance Conference (Budapest - External Event) — Speakers include Peter Carr & Thalesians workshop

Peter Carr

Peter Carr

Date and Time

24th, 25th & 26th June, 2015

Venue

Budapest

To sign up

You can register for this event and pay online at the WBS Training website: http://wbstraining.com/php/conferences/?id=67

Members of the Thalesians also have a special early bird discount code (contact Saeed Amen for details or click here on the Meetup.com event).

Highlights

The 1st Central & Eastern European Quant Finance Conference is priced to attract a regional as well as a global audience!

  • Peter Carr: Global Head of Market Modeling, Morgan Stanley: Derivatives Pricing under Bilateral Counterparty Default Risk: Path-Independent Probabilistic Valuation
  • Ashley Lester: Head of Fixed Income, Macro and Liquidity Research, MSCI: Trends in Banking Regulation and Model Validation
  • Carlo Acerbi: Head of Liquidity and Risk Methodologies Group, MSCI: Backtesting Expected Shortfall: Impact of Backtestability on Market Risk Regulation
  • Jan Novotny: Head of Research, Richfox Capital & Visiting Lecturer, Cass Business School: Trading Price Jump Clusters in FX Markets
  • Saeed Amen: Managing Director & Co-founder: THE THALESIANS: FX Volatility Over Events & Using Big Data To Trade Macro
  • Tamás Mátrai: Vice President, Credit Research, MSCI: Integrated Macro-Market-Credit Risk Framework
  • Professor Dariusz Gatarek: Polish Academy of Sciences: Credit Risk for Market Portfolios
  • Adriana Lelovska & Frantisek Kaliban: Senior Credit Risk Models Analyst, Erste Group Bank: Credit Risk Modelling of Low Default Portfolios - Bayesian Approach

Pre-Conference Workshop Day: Wednesday 24th June

  • Exploring Themes in Systematic Trading by Saeed Amen: Managing Director & Co-founder: THE THALESIANS
  • XVA, Margins and Capital by Massimo Morini: Head of Interest Rate & Credit Models, Banca IMI

Booking Fees

This conference is priced to attract a regional as well as a global audience!

Pre-Conference Workshop Day: Wednesday 24th June

  • €699.00 + HU VAT

The 1st Central & Eastern European Quant Finance Conference 25th & 26th June 2015

  • €999.00 + HU VAT

Early Bird Discount: 20% before 1st May 2015. Register to the Main Conference + Workshop and receive a €100 discount!

Conference Bookings: Discount Structure

  • Early Bird Discount: 20% Before 1st May
  • Early Bird Discount: 10% Before 29th May
  • Main Conference + Workshop (€100 Discount)
  • Receive an extra 5% discount when booking 3 or more delegates
  • 70% Academic Discount (FULL-TIME Students Only)
  • Use Thalesians early bird discount code (for a further 5% discount)

Behavioural Models & Sentiment Analysis: Applied to Finance (London - External Event) — Speakers including Hafez & Amen

Peter Hafez

Peter Hafez

Date and Time

15-16th July 2015

Venue

London

To sign up

You can register for this event and pay online at Unicom's website at http://conferences.unicom.co.uk/sentiment-analysis/programme.php

Abstract

Sentiment analysis has developed as a technology that applies machine learning and makes a rapid assessment of the sentiments expressed in news releases. News (events) move the market and are measured quantitatively. Analysts and investors digest financial news and their perceptions impact the market and move stock prices. This conference presents the current state of the art in this fast-emerging field. This is the 5th conference on this topic organized by UNICOM Seminars Ltd. The programme focuses on the application of Sentiment Analysis to the respective models of trading, fund management and risk control. Specialists in the domain present their recent research results, case studies and technology overviews. In particular the topic of Algorithmic Trading is addressed. Special features of this year’s conference are the inclusion of Social Media data (Twitter, blogs, Google Trends, online searches); how trustworthy these are and how they influence market sentiment, sentiment analysis for multiple asset classes.

Speakers include

  • Saeed Amen: Managing director and co-founder of the Thalesians.
  • Cristiano Arbex Valle: OptiRisk
  • Ashok Banerjee: Dean of New Initiatives and External Relations at IIM Calcutta
  • Svetlana Borokova: Associate professor of Quantitative Finance at the Vrije Universiteit Amsterda
  • James Cantarella: Global Proposition Manager for Enterprise Analytics at Thomson Reuters
  • Asher Curtis: Assistent Professor at University of Washington
  • Elijah DePalma: Quantitative research analyst for Thomson Reuters Machine Readable News group
  • Giuliano De Rossi: Head of European Quantitative Research team at Macquari
  • Dan diBartolomeo: President and founder of Northfield Information Services, Inc
  • Armando Gonzalez: President & CEO of RavenPack
  • Ilya Gorelik: CEO & Founder of Deltix, Inc.
  • Peter Hafez: Quant Research at RavenPack
  • Gary Kazantsev: R&D Machine Learning group at Bloomberg
  • Adrian Letchford: Research Fellow in Data Science at Warwick Business School
  • Raphael Markellos: Professor of Finance at Norwich Business School, University of East Anglia
  • Gautam Mitra: Founder and the MD of OptiRisk Systems
  • Richard Peterson: CEO of MarketPsych Data
  • Stephen Pulman: Professor of Computational Linguistics at the Department of Computer Science, Oxford University
  • Rajib Ranjan Borah: co-Founder and Director of iRageCapital Advisory Private Limited, and QuantInsti Quantitative Learning Private Limited
  • Xiang Yu: Business Development Techno Executive at OptiRisk Systems

Recent Events

IAQF-Thalesians Seminar (New York) — Dr. Andrew Kalotay — Tax-Efficient Trading of Municipal Bonds

Andrew Kalotay

Andrew Kalotay

Agenda

Thursday, May 14, 2015:

Venue

NYU Kimmel Center, Room 914, Kimmel Center, 60 Washington Square South, NY 10012, NY

Registration

Abstract

Although tax-loss selling is widely recognized as a potential enhancer of after-tax return, it is usually employed opportunistically, rather than as part of a comprehensive investment strategy. In particular, little attention is paid to determining the optimum time to execute, given transaction costs.

Municipal bonds provide an ideal asset class to appreciate the benefit of active tax management, because the tax-exemption of interest by itself does not guarantee tax-efficient performance. We will present a dynamic approach to maximize after-tax return, which includes structuring of the portfolio and optimizing the timing of trades. The key insight is that the right to make a tax-driven trade is a (tax) option, which is acquired automatically and at no cost with any purchase. The value of this option can be rigorously determined. Selling and reinvesting entails swapping the associated options. Thus the sale decision should factor in the net loss of option value. Our dynamic strategy is expected to improve after-tax return over buy-and-hold by 30-80 basis points annually, depending on the duration of the portfolio and on investor-specific considerations. The approach can be adapted to other asset classes, including common equity.

Speaker

Andrew Kalotay is a leading authority on the valuation of bonds and interest rate derivatives. He is a prolific contributor to the literature on topics ranging from advance refunding to tax-neutral valuation and tax management of municipal bond investments. His firm licenses fixed income valuation software and provides debt management advisory services.

Before establishing Andrew Kalotay Associates in 1990, Dr. Kalotay was with Salomon Brothers. Prior to Wall Street, he was at Bell Laboratories and AT&T. On the academic side, he was the founding director of the graduate Financial Engineering program at Polytechnic University (now part of NYU).

Dr. Kalotay holds a B.Sc. and M.Sc. from Queen's University and a Ph.D. from the University of Toronto, all in mathematics. He was inducted into the Fixed Income Analyst Society’s "Hall of Fame" in 1997.

IAQF-Thalesians Seminars

The IAQF-Thalesians Seminar Series is a joint effort on the part of the IAQF (formerly IAFE) and the Thalesians. The goal of the series is to provide a forum for the exchange of new ideas and results related to the field of quantitative finance. This goal is accomplished by hosting seminars where leading practitioners and academics present new work, and following the seminars with a reception to facilitate further interaction and discussion. The seminar series is limited to IAQF and Thalesians members only.

For older events, please see The Thalesians Quantitative Finance Seminars.

Puzzles

Masses and Buckets

You have M masses,  m_1, m_2, \ldots, m_M which you want to distribute across N buckets "as uniformly as possible". By this I mean that you are trying to minimise  \sum_{i=1}^N \sum_{j=i}^N (b_i - b_j)^2 , where bk is the sum of the masses in the k-th bucket. How would you achieve this?

To make this a little bit more concrete, suppose that I give you 20 masses, e.g. 23, 43, 12, 54, 7, 3, 5, 10, 54, 55, 26, 9, 9, 43, 54, 1, 8, 6, 38, 33. There are 4 buckets. How would you distribute the masses?

Please send your answers to paul, who happens to be at thalesians.com.

[ Solution ]

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