Homepage of Dr. Aleš Černý
 

Short bio

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 (full list here...)

[15]

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

[14]

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

[13]

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

[12]

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

[11]

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
[9]

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

[8]

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

[7]

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

[6]

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

[5]

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

[4]

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.
[1]

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)

[20]
17/07
2018
10th Bachelier Congress, Dublin
Convex Duality and Orlicz Spaces in Expected Utility Maximization
 
[19]
08/06
2017

*Convex Stochastic Optimization Workshop, Kings College London
Convex Duality and Orlicz Spaces in Expected Utility Maximization

[18]
03/11
2016

*London Mathematical Finance Seminar, UCL
Optimal Trade Execution Under Endogenous Pressure to Liquidate

[17]
28/08
2015

*George Boole Mathematical Sciences Conference, Cork
Quadratic Hedging With and Without Numeraire Change

[16]
25/09
2014

*London-Paris Bachelier Workshop, Paris
Good-deal Prices for Log Contract

[15]
04/06
2014

8th Bachelier Congress, Brussels
Asymptotics of Quadratic Hedging in Lévy Models

[14]
26/08
2013
6th Summer School of Mathematical Finance, Vienna
Computation of Optimal Monotone Mean-Variance Portfolios
[13]
05/09
2012
*Finance and Actuarial Science Talks, ETH Zurich
Optimal Hedging with Higher Moments
[12]
12/07
2010

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

[11]
24/06
2010

6th Bachelier Congress, Toronto
Admissible Strategies for Semimartingale Portfolio Optimization

[10]
18/07
2008

5th Bachelier Congress, London
Mean-Variance Hedging and Optimal Investment in Heston's Model

[9]
24/08
2007

EFA 2007 Annual Meeting, Ljubljana
Optimal Hedging with Higher Moments

[8]
25/05
2007

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

[7]
29/09
2005

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

[6]
28/09
2005

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

[5]
14/09
2005

*Summer School Bologna, Frontiers of Financial Mathematics, Bologna,
One-day workshop on the theory and applications of good-deal pricing

[4]
19/04
2005

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

[3]
24/09
2004

ESF Exploratory Workshop, London Business School
The Risk of Optimal, Continuously Rebalanced Hedging Strategies

[2]
23/05
2002

*Workshop on Incomplete Markets, Carnegie Mellon University, Pittsburgh
Derivatives without Differentiation

[1]
05/01
2001

AFA 2001 Annual Meeting, New Orleans
Generalized Sharpe Ratios

Refereeing Activity

Applied Mathematical Finance, Annals of Operations Research, Automatica, Bernoulli, Economic Journal, European Financial Management, European Journal of Finance, European Journal of Operational Research, Finance and Stochastics, IEEE Transactions on Automatic Control, International Journal of Computer Mathematics, International Journal of Theoretical and Applied Finance, Journal of Computational and Applied Mathematics, Journal of Computational Finance, Journal of Finance, Journal of Financial Econometrics, Journal of Futures Markets, Mathematical Finance, Mathematics and Financial Economics,  Mathematical Reviews, 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

[9]
09/2014
08/2018

Ján Komadel, Comenius University Bratislava
Optimization in financial mathematics

[8]
10/2011
10/2017

Juraj Špilda, Cass Business School
On Sources of Risk in Quadratic Hedging and Incomplete Markets

[7]
10/2013
09/2017

Xuecan Cui, Luxembourg School of Finance
Asset Pricing Models with underlying Lévy Processes

[6]
10/2008
10/2013

Nicolaos Karouzakis, Cass Business School
Three Essays on the Dynamic Evolution of Market Interest Rates…

[5]
10/2007
06/2012

Ka Kei Chan, Cass Business School
Theoretical essays on bank risk taking and financial stability

[4]
10/2006
11/2010

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

[3]
10/2002
10/2006

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

[2]
10/2001
09/2006

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

[1]
10/2001
10/2004

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

Media Coverage

[1]
01/03
2011

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

Other

  • 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 09/10/18