Homepage of Dr. Aleš Černý
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Short bio

My qualifications include BSc and MSc in Mathematical Engineering from the Czech Technical University in Prague, and a PhD in Economics from the University of Warwick (more details here). I have spent 7 years at Imperial College London, among others developing and teaching one of the core courses on the MSc in Finance programme. I am currently a full professor of finance at the Cass Business School, City University London and a visiting professor of mathematics at Comenius University Bratislava, Slovakia.

Research interests

The theory of asset pricing and risk measurement in incomplete markets is concerned with the methodology and practical implementation of optimal hedging and pricing of derivative securities in the presence of hedging errors. The standard asset pricing theory assumes that all sources of risk are priced in the market; this assumption is most famously embedded in the Black-Scholes option pricing formula. In reality, even extremely frequent hedging leaves a significant amount of risk. In most models this risk is unaccounted for, as LTCM found to its own detriment. My work proposes standardized measurement of risk across different utility functions, allows for attribution of performance among different assets (for example stocks and options) in a dynamic framework, and provides extremely fast implementation of optimal dynamic hedge ratios and risk measurements using Fourier transform.

Selected publications (more publications and supplementary materials available here...)


with Pavol Brunovský and Ján Komadel, Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory and Numerical Solutions, European Journal of Operational Research,  264(3), 1159-1171, 2018


with Fabio Maccheroni, Massimo Marinacci and Aldo Rustichini, On the Computation of Optimal Monotone Mean-Variance Portfolios Via Truncated Quadratic Utility, Journal of Mathematical Economics 48(6), 386-395, 2012


with Chris Brooks and Joelle Miffre, Optimal Hedging with Higher Moments, Journal of Futures Markets 32(10), 909-944, 2012


with Ioannis Kyriakou, An Improved Convolution Algorithm for Discretely Sampled Asian Options, Quantitative Finance 11(3), 381-389, 2011


with Sara Biagini, Admissible Strategies in Semimartingale Portfolio Optimization, SIAM Journal on Control and Optimization, 49(1), 42-72, 2011

[10] Mathematical Techniques in Finance: Tools for Incomplete Markets, Princeton University Press, 2nd edition, July 2009, pp. 416
  • hands-on introduction to asset pricing, optimal portfolio selection and evaluation of investment performance
  • simple EXCEL spreadsheets and MATLAB codes integrated in the text
  • large number of examples and solved exercises
  • more advanced topics include
    • fast Fourier transform
    • finite difference methods
    • multinomial lattices and Levy processes

with Jan Kallsen, Hedging by Sequential Regressions Revisited, Mathematical Finance 19(4), 591-617, 2009


with Jan Kallsen, Mean-Variance Hedging and Optimal Investment in Heston's Model With Correlation, Mathematical Finance 18(3), 473-492, 2008


with Jan Kallsen, A Counterexample Concerning The Variance-Optimal Martingale Measure, Mathematical Finance 18(2), 305-316, 2008


with Jan Kallsen, On The Structure of General Mean-Variance Hedging Strategies, The Annals of Probability 35(4), 1479-1531, 2007


Optimal Continuous-Time Hedging with Leptokurtic Returns, Mathematical Finance, 17(2), 175-203, 2007.


with David K. Miles, Risk, Return and Portfolio Allocation Under Alternative Pension Systems with Incomplete and Imperfect Financial Markets, The Economic Journal, 116(2), 529-557, 2006.

[3] Introduction to Fast Fourier Transform in Finance, Journal of Derivatives, 12(1), 73-88, 2004
[2] Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets, European Finance Review, 7(2), 191-233, 2003. Presented at AFA Annual Meeting 2001, New Orleans.

with Stewart D. Hodges, The Theory of Good-Deal Pricing in Financial Markets, in Geman, Madan, Pliska, Vorst (eds.): Mathematical Finance -- Bachelier Congress 2000, 175-202, Springer Verlag 2002.

Research Projects

  • with Prof. David Miles, 2000-2004, Economics of Social Security in Japan, £200,000+
  • with Prof. James Sefton, 2002-2004, Design of Behavioural Tax Model, £80,000

Selected refereed conferences and *invited talks (full list here)


AnStaP10, Conference in Honour of W. Schachermayer, Vienna, Admissible Strategies for Semimartingale Portfolio Optimization


Sixth Bachelier Congress, Toronto, Admissible Strategies for Semimartingale Portfolio Optimization


Fifth Bachelier Congress, London, Mean-Variance Hedging and Optimal Investment in Heston's Model with Correlation


EFA 2007 Annual Meeting, Ljubljana, Optimal Hedging with Higher Moments


*Stanford Unversity, Mean-Variance Hedging and Optimal Investment in Heston's Model with Correlation


*Courant Institute for Mathematical Sciences, NYU, On the Structure of General Mean-Variance Hedging Strategies


*Columbia University, New York, On the Structure of General Mean-Variance Hedging Strategies


*Summer School Bologna, Frontiers of Financial Mathematics - Pricing Derivatives in Incomplete Markets, Bologna, Leader of one-day workshop on the theory and applications of good-deal pricing


*Developments in Quantitative Finance, Isaac Newton Institute, Cambridge, On the Structure of General Mean-Variance Hedging Strategies


European Science Foundation Exploratory Workshop on Dynamic Portfolio Choice, Asset Pricing and Mathematical Finance, London Business School, The Risk of Optimal, Continuously Rebalanced Hedging Strategies and Its Efficient Evaluation via Fourier Transform


*Workshop on Incomplete Markets, Center for Computational Finance, Carnegie Mellon University, Pittsburgh, Derivatives without Differentiation


AFA 2001 Annual Meeting, New Orleans, Generalized Sharpe Ratios

Refereeing Activity

Applied Mathematical Finance, Annals of Operations Research, Automatica, Bernoulli, European Financial Management, IEEE Transactions on Automatic Control, International Journal of Theoretical and Applied Finance, Journal of Computational and Applied Mathematics, Journal of Computational Finance, Journal of Finance, Journal of Financial Econometrics, Mathematical Finance, Mathematics of Operations Research, Operations Research, Princeton University Press, Quantitative Finance, Review of Derivatives Research, Risk, SIAM Journal on Financial Mathematics, Statistics and Decisions

Editorial Appointments

06/2007- Review of Derivatives Research

PhD Supervision


Ioannis Kyriakou, Efficient valuation of exotic derivatives with path-dependence and early-exercise features, Cass Business School


Lubomir Schmidt, , Optimal life-cycle consumption and asset allocation with applications to pension finance and public economics, Imperial College Business School


Mariam Harfush-Pardo, An investigation on portfolio choice and wealth accumulation in fully funded pension systems with a guaranteed minimum benefit, Imperial College Business School


Yung-Chih Wang, Topics in investment appraisal and real options, Imperial College Business School

Media Coverage


Hospodarske Noviny, Slovák, ktorý vie vypocítat riziká pri obchodovaní na burze


  • Erdos Number: 5 (AC --> S.D. Hodges --> P.G. Moore --> N.L. Johnson --> C.A. Rogers --> PE)
  • Kolmogorov Number: 3 (AC --> J. Kallsen --> A.N. Shiryaev --> ANK)

Last revised 01/03/11