publications  and  research output

Pre-pubs, submitted and working papers

[] D. Wilcox and T. Gebbie, Factorising equity returns in an emerging market through exogenous shocks and capital flowshttp://arxiv.org/abs/1306.5302; http://dx.doi.org/10.2139/ssrn.2283486

[] D. Wilcox and T. Gebbie, Hierarchical Causality in Financial Economics, http://arxiv.org/pdf/1408.5585.pdf

[] D. Wilcox, No such thing as a risk-neutral market, http://arxiv.org/abs/1602.08429 [q-fin GN] 

[] D. Wilcox, On growth cycles in a two-tier economy, working paper distrubuted in 2013, presented at QuERILAB research seminar 24 July 2015, 5 pages

Peer-reviewed publications 

[17] M. Harvey, D. Hendricks, T.Gebbie and D. Wilcox, Deviations in expected price impact for small transaction volumes under fee restructuring, Physica A (2017)


[16] D. Hendricks, T.Gebbie and
D. Wilcox, Detecting intraday financial market states using temporal clustering, Quantitative Finance; DOI 10.1080/14697688.2016.1171378 (online; 30 pages) http://www.tandfonline.com/doi/abs/10.1080/14697688.2016.1171378?journalCode=rquf20

[15] D. Hendricks, D. Wilcox and T.Gebbie, High-speed detection of emergent clustering via an unsupervised parallel genetic algorithm, SA J. of Science, Vol 112, Issue 1 /2;  http://arxiv.org/pdf/1403.4099.pdf


[14] D. Wilcox and T. Gebbie, On Pricing Kernels, Information and Risk,
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2340465 Investment Analysts Journal 44:1, 1-19 (2015),  http://www.tandfonline.com/doi/pdf/10.1080/10293523.2014.994437

[13] D. Hendricks and D. Wilcox, A reinforcement learning extension to the Almgren-Chriss framework for optimal trade execution, Computational Intelligence for Financial Engineering & Economics (CIFEr), IEEE Conference, March 2014, 457-464, doi: 10.1109/CIFEr.2014.6924109,  http://arxiv.org/pdf/1403.2229.pdf


[12] D. Wilcox, A Personal Reflection on Advancing in South African Academic Science, Chapter 3, Vignette 3.3 in Advancing Women in Science, Edited by W. Pearson, L. Frehill and C. McNeely, Springer International, 2015, http://www.springer.com/us/book/9783319086286

[11] D. Wilcox, Essential Spectra of Linear Relations, Linear Algebra and Applications, Vol. 462, 110-125 (2014), http://arxiv.org/pdf/1304.3801.pdf
 
[10] V. Konlack-Sognia and D. Wilcox, A comparison of generalised hyperbolic distributions for equity returns, Journal of Applied Mathematics, 
http://dx.doi.org/10.1155/2014/263465

[9] T. Álvarez and D. Wilcox, The Baire property and the domain of iterates of a paracomplete linear relation,
Journal of Operator Theory, 66:2, 451–464 (2011)

[8] D. Wilcox, T. Gebbie, Periodicity and scaling of eigenmodes in an emerging market, International Journal of Theoretical and Applied Finance, 11, 7, 739-760 (November 2008), http://arxiv.org/abs/cond-mat/0404416 

[7] D. Wilcox, T. Gebbie, An analysis of cross correlations in South African market data, Physica A, Volume 375, Issues 2,  Pages 584-598 (2007), http://arxiv.org/abs/cond-mat/0402389 

[6] T. Álvarez  and D. Wilcox, Perturbation theory of multivalued Atkinson operators in normed spaces, Bull.Austral.Math.Soc., Vol. 76  (2007), 195-204

[5] D. Wilcox, T. Gebbie, On the analysis of cross correlations in South African market data, Physica A, Volume 344, Issues 1-2,  Pages 294-298 (2004)

[4] T. Álvarez , R.W. Cross, D. Wilcox, Adjoint Characterisations of Quasi-weakly Compact Linear Relations (with),    J. Math. Anal. Appl., 277 (2002) 257-271

[3]  R.W. Cross and D. Wilcox, Multivalued Linear ProjectionsQuaestiones Mathematicae, 25 (2002) 503-512

[2] T. Álvarez , R.W. Cross and D. Wilcox, Quantities related to upper and lower semi-Fredholm type linear relations, Bull. Austral. Math. Soc. Vol. 66 (2002), 275-289.

[1] T. Álvarez , R.W. Cross and D. Wilcox,  Multivalued Fredholm type Operators with Abstract Generalised Inverses,  J. Math. Anal. Appl.  261 (2001), 403-417.

    Paper [1] was my first research manuscript output. It originally covered both the characterisation and perturbation of Atkinson relations, where the contents of paper [5] made up the second part of this focus. The results of this research were my original work and were central to my PhD thesis. I rewrote paper [1] substantially after an earlier draft was rejected without much comment from another journal. Paper [1], however, contained an error, which was corrected in my phd thesis (linked below). Clarification of my actual contributions to publications [1-5, 8] are given in the notes and remarks at the end of corresponding chapters in my thesis.  


PhD (Dec 2002) 

·         PhD research proposal (May 1998, proposal to upgrade based my MSc dissertation at that time, which contained original material)

·         Multivalued Semi-Fredholm Operators in Normed Linear Spaces (first published Dec 2001; graduated Dec 2002)

 

A selection of old  presentations, teaching notes and science communications (a more comprehensive list of presentations is included in my CV)

·         On mathematics education in South Africa & the relevance of popularising mathematics (1999, edited Aug  2003).This article arose as an exercise to clarify and summarise my understanding of the forces which have shaped mathematics education in South Africa. It served to take a snapshot of the status of developments at the time (1999) and the impact of legislation which served to suppress the development of sections of the SA population under Apartheid.

·         Matrices for school learners / Mathematics for computer games (2004): This presentation introduces matrices to high-school level learners, with attention to some of the techniques used for computer gaming graphics. This talk was presented at a UCT Dept Mathematics & Applied Mathematics information programme for school learners (organised by Gilmour and Webb) and to a hall of Academy of Mathematics, Science and Technology high school learners who participated actively by providing answers to calculations on the slides, Tokai, Western Cape.  

·         Introduction to the Black-Scholes-Merton PDE (2005) I prepared these lecture notes on the derivation and solution of the Black-Scholes-Merton (BSM) model to teach introductory-level pricing of derivative securities from the perspective of PDE methods (separation of variables, integral transform methods, pricing and model limitations). Since then, I have taught the martingale approach to obtaining the same result as well as more generally financial modeling considerations. From a research perspective, I commenced with investigating applications of random matrix theory to the estimation of cross-correlations. 

·         On the Malliavin-Mancino-Fourier Method for Estimation of Cross-Correlations (2005/2006), based on work with MSc student, Chanel Malherbe and Tim Gebbie [slides in Openoffice before Beamer days]

·         SET presentation to Grade 11 female school learners (2006), presented in hour talk/info session with about 25 high school learners at an Eskom Girl Learner Programme in Parrow, Cape Town

·         An interdisciplinary approach to quantitative finance  (2004-2007)

·         Mathposter_by_DWilcox (2007): This is a general mathematics poster designed for science and math information days in 2007 which I made for the SAWISE Celebration of Women in Science, Iziko Museum, Aug 2007 and the SAWISE booth of the UCT Science Information day hosted at South Peninsula Senior Secondary in that same year. While the design is my own, the sub-topic descriptions  are based on centuries of accumulated knowledge and are not my describing my own research. The idea to include an interactive component was original (the chaos game itself is due to R.L.Devaney and co-authors ). I was motivated by the objective to provide content for interactive information tables at science days. 

·         Complexity theory and the science of finance (2007) (with Tim Gebbie), Business Report, 9 May 2007. This article was in preparation during 2006 and preceded the commonly accepted commencement of the financial crisis (Aug 2007+). The views were based on the empirical    observations obtained from papers [6-7] above.

·         The factorisation of equity returns in an emerging market (2007) and Factorisation of equity returns in an emerging market (2008)

·         Evidence of characteristic cross-sectional pricing of stock returns in South Africa (2007/2008)

·         Faking value and Size (2008) (with Tim Gebbie), Collective Insights, special issue of Financial Mail, 2008. This article demonstrates that it is possible to obtain results which illustrate that portfolios contructed according to so-called value and small investment paradigmes can stocks can outperform the market even in a simulation environment, where all stocks are simply Gaussian random processes.

·         A review of the global financial crisis  (2009) - Research seminar presented to the AMF research group

·         Clustering dynamics through an emerging market crash in the global crisis (2009), presented at the International Workshop on Coping with Crises in Complex Socio-Economic Systems, 2009

·         A review of the development of multivariate equity models for derivative valuation, also presented to the School of Actuarial Science, Wits (2010)

·         Spin, stochastic factor models and a GA (2010). 

·         WISEr for it  (2011),   Women in Science, Engineering  and Technology 

·         High performance computing via GPU parallelisation (April, 2011), part of this talk was presented in an Optinum Seminar on the Matlab parallel and distributed toolboxes for high performance computing in finance. 

·         Autocorrelation and response in high frequency trades on the JSE and BM&FBOVESPA (2011)