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From Damiano Brigo

[edit]

I think the intentions are good, but the page as is contains a couple of inaccuracies: I had my PhD in Amsterdam, not in Padua, and the career description lacks the years I spent in Banca IMI, where I wrote most of my works in Mathematical Finance.

Furthermore, I am not sure about inclusion in (Italian) Mathematicians, or Economists, or other cathegories. I may have the CV of an average professor in applied mathematics and I am known as a mathematician in the financial industry and a little in the automatic controls industry, but I don't think I should be listed among mathematicians from history such as those in the list. I will proceed with edits to reduce its importance.

Thanks and Kind Regards

Damiano Brigo - d dot brigo at imperial dot ac dot uk

— Preceding unsigned comment added by D.brigo (talk • contribs) 18:44, 9 January 2009 (UTC)[reply]

Updates

[edit]

Added minimal updates but still not sure about this page

Damiano Brigo - damiano dot brigo at imperial.ac.uk — Preceding unsigned comment added by Damianobrigo (talk • contribs) 15:29, 23 September 2014 (UTC)[reply]

Edit request 19 May 2023

[edit]

I would like to request an edit for this page about me. As you see from the history above I had to correct quite a few mistakes in the past and I wasn't even sure about the page but now I am more oriented to think it makes sense as I hope will be clear from the material. The last update was 10 years ago and the information on the page is out of date. I will do my best to maintain a neutral stance and to provide secondary sources. I will of course be open to the Editors decisions and recommendations.

What I will do: I will propose below an edited version of the page, explaining later the edits reasons.

Edit request

PROPOSED EDITED VERSION: BEGIN

Damiano Brigo (born Venice, Italy 1966) is a mathematician and Chair in Mathematical Finance at Imperial College London. He is known for research in filtering theory, mathematical finance, stochastic analysis, probability theory and statistics.

Level 2 section header: Main contributions

Level 3 section header: Nonlinear Filtering

Brigo started his work with the development, with Bernard Hanzon and Francois Le Gland (1998), of the projection filters, a family of approximate nonlinear filters based on the differential geometry approach to statistics, also related to information geometry.[1][2][3]

The basic idea of projection filters is projecting the stochastic partial differential equation (SPDE) characterizing the optimal nonlinear filter, whose solution is typically infinite dimensional, onto a finite dimensional manifold of probability densities, thus reducing the SPDE to a finite dimensional stochastic differential equation. In the initial works it was shown that by choosing a suitable exponential family as manifold, the correction step approximation in the filtering algorithm can be made exact by the projection[1]. Furthermore, it was shown that, when projecting on an exponential family, the projection filter would coincide with the earlier assumed density filters for the moments of the sufficient statistics of the exponential family[2]. The projection filter was tested against a numerical implementation of the optimal filter for the cubic sensor system[1], showing that it could track effectively bimodal densities that would be hard to approximate with more standard algorithms like the extended Kalman filter. This initial work on the projection filter was then developed further both by Brigo and co-authors and by different authors, in several sub-fields of filtering, including applications to quantum systems. More specifically, Jones and Soatto (2011) mention projection filters as possible algorithms for on-line estimation in visual-inertial navigation[4], mapping and localization, while again on navigation Azimi-Sadjadi and Krishnaprasad (2005)[5] use projection filters algorithms. The projection filter has been also considered for applications in ocean dynamics by Lermusiaux 2006[6]. Kutschireiter, Rast, and Drugowitsch (2022)[7] refer to the projection filter in the context of continuous time circular filtering. For quantum systems applications, see for example van Handel and Mabuchi (2005)[8] and Gao, Zhang and Petersen (2019)[9]. Ma, Zhao, Chen and Chang (2015) refer to projection filters in the context of hazard position estimation, while Vellekoop and Clark (2006)[10] generalize the projection filter theory to deal with changepoint detection. Harel, Meir and Opper (2015)[11]apply the projection filters in assumed density form to the filtering of optimal point processes with applications to neural encoding. Broecker and Parlitz (2000)[12] study projection filter methods for noise reduction in chaotic time series. Zhang, Wang, Wu and Xu (2014) [13] apply the Gaussian projection filter as part of their estimation technique to deal with measurements of fiber diameters in melt-blown nonwovens. Most of the above applications refer to the original projection filters [1][2] described above. In Armstrong and Brigo (2016)[14] a new metric is adopted for the projection filter, connecting the projection filters on families of mixture distributions with Galerkin methods, while Armstrong, Brigo and Rossi Ferrucci (2021)[15] derive optimal projection filters that satisfy specific optimality criteria in approximating the optimal filter. This is based on research on the geometry of Ito Stochastic differential equations on manifolds based on the jet bundle, the so called 2-jet interpretation of Ito stochastic differential equations on manifolds, referred below in the stochastic analysis section.

Level 3 section header: Mathematical Finance

Overall, the area of mathematical finance is the subject where Brigo has been most active, authoring about one hundred publications. Brigo has been the most cited author in the technical section of the industry influential Risk Magazine in the twenty years 1998-2018.[16] He also authored several columns for Risk Magazine on a number of areas related to his research described below[17][18][19][20][21]. Brigo is also mostly know for his extensive work on interest rate derivatives and his joint book with Fabio Mercurio on interest rate models[22] for derivatives markets, a book with thousands of citations[23] and widely adopted by academics and industry practitioners. The book devotes particular attention to both the theory and practice of interest rate modelling, including inflation, credit risk and calibration of interest rate models to liquid derivatives data for a variety of models, collecting also original research by the two authors. More generally, Brigo and co-authors have shown how to construct stochastic differential equations consistent with mixture models, both in the univariate and multivariate setting, applying this to volatility smile modeling in the context of local volatility models.[24][25][26][27][28] Since 2002, Brigo contributed to credit derivatives modeling and counterparty risk valuation. Brigo and co-authors worked extensively on credit default swap options or credit default options in particular[29][30], both for single name default options and credit default index options[31]. Brigo worked extensively also on the theory and practice of valuation adjustments with several co-authors, first introducing early counterparty risk pricing calculations (later called credit valuation adjustment - CVA)[32] and then focusing on wrong way risk for CVA[33]. Brigo focused also on multiname credit derivatives, showing with Pallavicini and Torresetti (2007)[34] how data implied non-negligible probability that several names defaulted together, showing some large default clusters and a concrete risk of high losses in collateralized debt obligations prior to the financial crisis of 2007–2008. This work has been further updated in 2010 leading to a volume for Wiley[35], while a volume on the updated nonlinear theory of valuation, including credit effects,[36] collateral modeling and funding costs, has appeared in 2013. The research on this theme continued with several academic papers that contributed to make the valuation adjustment theory fully rigorous mathematically, including Brigo, Buescu, and Rutkowski (2017)[37] for a way to reconcile credit and funding effects with a basic option pricing theory; Brigo, Francischello and Pallavicini (2019)[38] for the expression of valuation as a fully nonlinear problems through backwards stochastic differential equations and semi-linear partial differential equations; Brigo, Buescu, Francischello, Pallavicini and Rutkowski (2022)[39], to reconcile the mathematically rigorous results on nonlinear valuation and valuation adjustments based on cash flows adjustments with an approach based on hedging. Brigo and co-authors also contributed to a pathwise approach to finance, where probability is not used. Armstrong, Bellani, Brigo and Cass (2022)[40] show how to obtain option prices without probability theory, using rough paths techniques. This idea originated from an old result by Brigo and Mercurio (2000)[41] where it is shown that given an however fine trading time grid, two statistically indistinguishable models in the grid can generate arbitrarily different options prices. Still in the context of pathwise finance, Bellani and Brigo (2022)[42] show how one can do optimal trade execution in a model agnostic way, introducing the notion of good execution. Brigo, Graceffa and Neumann (2022)[43] show how to combine the theories of price impact, related to optimal execution, with the theory of the term structure of interest rates. In the space of risk measures, Armstrong and Brigo (2019, 2022)[44][45] show that, under the S-shaped utility of Kahneman and Tversky, which can be used to model excessively tail risk seeking traders, or limited liability traders, static risk constraints based on value at risk or expected shortfall as risk measures are ineffective in curbing the potentially rogue trader utility maximization. This result was discussed also in the mainstream Financial Times magazine, The Banker[46]. In the space of retail credit risk, in the specific little investigated area of non-performing loans, Bellotti, Brigo, Gambetti and Vrins (2021)[47] also worked on prediction of recovery rates with machine learning. Still in the broad area of artificial intelligence applied to finance and insurance, Lamberton, Brigo and Hoy (2017)[48] illustrate how robotic process automation and artificial intelligence can be used to improve performances in the insurance industry.

Level 3 section header: Stochastic Analysis, Probability, Statistics, Rough Paths and Geometry

Brigo has been working on several aspects of probability theory and statistics. His main interest has been at the intersection between stochastic differential equations and the geometry of manifolds, which he applied initially to filtering but studied and researched later in their own right. The main result is an interpretation of Ito Stochastic Differential Equations (SDEs) related to Schwartz morphism and developed with John Armstrong, using the notion of jet bundle in differential geometry, bringing the identification of SDEs with 2-jets[49]. In probability and statistics, with Aurelien Alfonsi (2005)[50], Brigo introduced new families of multivariate distributions in statistics through the periodic copula function concept. Brigo, Mai and Scherer (2016)[51] introduce a new characterization of the Marshall-Olkin distribution based on indicators of a Markov Chain. Brigo became also interested in the theory of Peacocks, particular stochastic processes, and obtained results on them in Brigo, Jeanblanc and Vrins (2020)[52], linking them with Stochastic Differential Equations whose solutions are uniformly distributed. Finally, Armstrong, Brigo, Cass and Rossi Ferrucci (2022)[53] show how to study non-geometric rough differential equations and rough paths on manifolds, extending the theory for geometric rough paths. Brigo and co-authors also applied rough paths to option pricing as explained in the Mathematical Finance part.

Level 2 section header: Career, current and past affiliations

Brigo was appointed Chair in Mathematical Finance at the Department of Mathematics of Imperial College London in 2012[54]. He has been also Director of the Capco Institute[54]. He was in the academic advisory board of several financial institutions and regularly presented seminars and training to financial institutions, regulators and central banks. {Note to Editors: I have proof of this in the form of contracts, but there is no online reference to these events. I can send a list of talks and seminars and appointments if requested but I don't know what value this would have}. He previously held the Gilbart Chair of Financial Mathematics at King's College London (2010-2012), as indicated in the profile article in Risk Magazine[55] and worked as Managing Director at Fitch Solutions in London (2007-2010)[55] and previously as head of credit models in Banca IMI in Milan[55]. He holds a PhD in Stochastic Nonlinear Filtering with Differential Geometric Method from the Free University of Amsterdam.

[References]

Level 2 section header: External links

[End matter]

PROPOSED EDITED VERSION - END

Explanation of edits and reasons

  1. I would remove "applied" from "applied mathematician" because my research has touched pure mathematics areas in the last ten years (jet bundle interpretation of SDEs, projection of SDEs on submanifold, Non-geometric Rough paths on manifolds, Peacock processes, etc, see references added and new sections added).
  2. I would change "He is known for research in filtering theory and mathematical finance" to "He is known for research in filtering theory, mathematical finance, stochastic analysis, probability and statistics". I became active in all these areas and I will provide references for it.
  3. I would edit "Main Results" into "Main contributions"
  4. Description of main results. This is a major edit, but the page as is now is really outdated. I have developed work in several subfields that weren't even mentioned previously. The works would be better visible with a division in areas, as the reader would be able to contextualize further, so I did this. If this is accepted, I will link other articles of Wikipedia here. For example, the article on the filtering problem mentions projections filters, that are now briefly explained here. I could link to the page. I also tried to add citations to our work coming from other authors, especially in filtering, where I already had a report of the Swedish Army as a secondary source, or some examples of mainstream sources like The Banker or Risk Magazine for finance, to show that the research had impact outside academia. I have updated the most cited author feature of Risk Magazine, because I achieved it for the 20 years 1998-2018. I haven't mentioned quite a number of other results, so this is really a summary, if more extensive than the previous one.
  5. On affiliations I tried to find as much as possible online. I found printed articles in Risk Magazine that confirm my affiliation to King's College, Fitch, Banca IMI. I also found a Finextra article commenting on being appointed as director of the Capco institute and on being a professor at Imperial College London. I have been affiliated with several other financial institutions in advisory boards but I can't find links online. I have proof I could send privately to Editors but I imagine this is not the procedure?
  6. I removed the list of relevant publications sections as these are now all directly cited in the text, which is better I think.
  7. In the past, when I corrected the page mistakes the first time and reduced it considerably, I was told I cannot put too many primary citations and need to have secondary ones too. I did that at the time and I tried to do that here again, adding many references from other authors to a good part of my work.
  8. I haven't been exemplary in formatting everything, especially references but I would be interested in the Editors opinion before doing further work.
  9. I added my Google Scholar page, and I referred to it for the number of citation of my book "Interest Rate Models". This book is one of the works that made me most known in both academia and industry but the only way I have to show it is the number of citation in Google Scholar. Risk Magazine published a review of the book too but it is very old and refers to the first edition, so I haven't included it.
  10. I removed the banner from "Career" as I now provided a number of references, I hope they are sufficient.

— Preceding unsigned comment added by DamianoBrigo2 (talk • contribs) 18:53, 10 June 2023 (UTC)[reply]

  1. I thank the Editors in advance for checking this and letting me know.

— Preceding unsigned comment added by DamianoBrigo2 (talk • contribs) 21:47, 19 May 2023 (UTC)[reply]

Formatted and cleaned up (including removal of actual section headers in edit request) Tol (talk | contribs) @ 23:37, 25 May 2023 (UTC)[reply]
Request's references

References

  1. ^ a b c d Brigo, Damiano; Hanzon, Bernard; LeGland, Francois (1998). "A differential geometric approach to nonlinear filtering: the projection filter". IEEE Transactions on Automatic Control. 43 (2): 247–252.
  2. ^ a b c Brigo, Damiano; Hanzon, Bernard; LeGland, Francois (1999). "Approximate nonlinear filtering by projection on exponential manifolds of densities". Bernoulli. 5 (3): 407–430.
  3. ^ Swedish Defense Research Agency Scientific Report, http://www.foi.se/ReportFiles/foir_1074.pdf Archived 2016-03-03 at the Wayback Machine.
  4. ^ Jones, Eagle S; Soatto, Massimo (2011). "Visual-inertial navigation, mapping and localization: A scalable real-time causal approach". The International Journal of Robotics Research. 30 (4): 407–430.
  5. ^ Azimi-Sadjadi, Babak; Krishnaprasad, P.S. (2005). "Approximate nonlinear filtering and its application in navigation". Automatica. 41 (6): 945–956.
  6. ^ Lermusiaux, Pierre F. J (2006). "Uncertainty estimation and prediction for interdisciplinary ocean dynamics". Journal of Computational Physics. 217 (1): 176–199.
  7. ^ Kutschireiter, Anna; Rast, Luke; Drugowitsch, Jan (2022). "Projection filtering with observed state increments with applications in continuous-time circular filtering". IEEE Transactions on Signal Processing. 70.
  8. ^ van Handel, Ramon; Mabuchi, Hideo (2005). "Quantum projection filter for a highly nonlinear model in cavity QED". Journal of Optics B: Quantum and Semiclassical Optics. 7.
  9. ^ Gao, Qing; Gao, Guofeng; Petersen, Ian R (2019). "An exponential quantum projection filter for open quantum systems". Automatica. 99: 59–68.
  10. ^ Vellekoop, M. H.; Clark, J. M. C. (2006). "A nonlinear filtering approach to changepoint detection problems: Direct and differential-geometric methods". SIAM Review. 48 (2): 329–356.
  11. ^ Harel, Yuval; Meir, Ron; Opper, Manfred (2015). "A tractable approximation to optimal point process filtering: Application to neural encoding". Advances in Neural Information Processing Systems. 28.
  12. ^ Broecker, Jochen; Parlitz, Ulrich (2000). "Noise reduction and filtering of chaotic time series". Proc. NOLTA 2000.
  13. ^ Zhang, Xian Miao; Wu Wang, Rong; Xu, Bugau (2014). "Automated measurements of fiber diameters in melt-blown nonwovens". Journal of Industrial Textiles. 43 (4): 593–605.
  14. ^ Armstrong, John; Brigo, Damiano (2016). "Nonlinear filtering via stochastic PDE projection on mixture manifolds in L2 direct metric". Mathematics of Control, Signals and Systems. 28 (1): 1–33.
  15. ^ Armstrong, John; Brigo, Damiano; Rossi Ferrucci, Emilio (2019). "Optimal approximation of {SDE}s on submanifolds: the Ito-vector and Ito-jet projections". . Proceedings of the London Mathematical Society. 119 (1): 176–213.
  16. ^ Degrees of Influence, Risk Magazine, December 2018, pp. 129, Table B.
  17. ^ Damiano Brigo, Model risk in the transition to risk-free rates, Risk Magazine, June 5, 2018.
  18. ^ Damiano Brigo, Simple models won't cut it for systemic risk, Risk Magazine, May 8, 2018.
  19. ^ Damiano Brigo, Curbing rogue behaviour, April 9, 2018.
  20. ^ Damiano Brigo, XVA: back to CVA? Risk Magazine, March 20, 2018.
  21. ^ Damiano Brigo, Time to move on from risk-neutral valuation? Risk Magazine, Feb 8, 2018.
  22. ^ Brigo, Damiano; Mercurio, Fabio (2006). Interest rate models: theory and practice. Heidelberg: Springer-Verlag.
  23. ^ https://scholar.google.co.uk/citations?user=65wdZxAAAAAJ&hl=en>
  24. ^ Fengler, M. R. (2005), Semiparametric modeling of implied volatility, Springer Verlag, Berlin.
  25. ^ Musiela, M., and Rutkowski, M. (2004), Martingale Methods in Financial Modelling, 2nd Edition, Springer Verlag, Berlin.
  26. ^ Brigo, D. and Mercurio, F (2002). Lognormal-mixture dynamics and calibration to market volatility smiles. International Journal of Theoretical and Applied Finance, Vol 5, Pages 427 - 446
  27. ^ Brigo, D, Mercurio, F, Sartorelli, G, Alternative asset-price dynamics and volatility smile, QUANT FINANC, 2003, Vol: 3, Pages: 173 - 183
  28. ^ Brigo, D., Rapisarda, F., and Sridi, A. (2018). The multivariate mixture dynamics: Consistent no-arbitrage single-asset and index volatility smiles. IISE TRANSACTIONS, 50(1), 27-44. doi:10.1080/24725854.2017.1374581
  29. ^ Damiano Brigo (2005). Market Models for CDS Options and Callable Floaters, Risk Magazine, January 2005 issue.
  30. ^ Damiano Brigo, Aurelien Alfonsi (2005). Credit Default Swap Calibration and Derivatives Pricing with the SSRD Stochastic Intensity Model, Finance and Stochastic (2005), Vol. 9, N. 1.
  31. ^ Damiano Brigo and Massimo Morini (2011). No-Armageddon Arbitrage-free Equivalent Measure for Index options in a credit crisis. Mathematical Finance, Vol. 21, Issue 4, pp. 573-593
  32. ^ Brigo, D., and Masetti, M. (2006). Risk Neutral Pricing of Counterparty Risk. Chapter 11 In: Pykhtin, M. (Editor), Counterparty Credit Risk Modelling: Risk Management, Pricing and Regulation (2006). Risk Books, London
  33. ^ Damiano Brigo and Andrea Pallavicini (2007). Counterparty Risk under Correlation between Default and Interest Rates. In: Miller, J., Edelman, D., and Appleby, J. (Editors), Numerical Methods for Finance, Chapman Hall
  34. ^ Damiano Brigo, Andrea Pallavicini, Roberto Torresetti (2007). Cluster-based extension of the generalized Poisson loss dynamics and consistency with single names. International Journal of Theoretical and Applied Finance, Vol 10, n. 4.
  35. ^ Damiano Brigo, Andrea Pallavicini and Roberto Torresetti: Credit Models and the Crisis: A journey into CDOs, Copulas, Correlations and Dynamic Models , Wiley, 2010.
  36. ^ Has Basel got its numbers wrong? The Banker, Financial Times weekly supplement, June 21, 2011.
  37. ^ Brigo, D., Buescu, C., and Rutkowski, M. (2017). Funding, repo and credit inclusive valuation as modified option pricing. OPERATIONS RESEARCH LETTERS, 45(6), 665- 670. doi:10.1016/j.orl.2017.10.009
  38. ^ Brigo D., Francischello M., Pallavicini A. (2019). Nonlinear valuation under credit, funding, and margins: existence, uniqueness, invariance, and disentanglement. European Journal of Operational Research, Vol: 274, Pages: 788-805
  39. ^ Damiano Brigo, Cristin Buescu, Marco Francischello, Andrea Pallavicini and Marek Rutkowski (2022). Nonlinear Valuation with XVAs: Two Converging Approaches. Mathematics 10(5)
  40. ^ John Armstrong, Claudio Bellani, Damiano Brigo and Thomas Cass (2021). Option pricing models without probability: a rough paths approach. Mathematical Finance, vol. 31, pages 1494–1521.
  41. ^ Damiano Brigo and Fabio Mercurio (2000). Option Pricing Impact of Alternative Continuous Time Dynamics for Discretely Observed Stock Prices, Finance and Stochastics, Vol. 4 issue 2, pages 147-159
  42. ^ Claudio Bellani and Damiano Brigo (2020). Mechanics of good trade execution in the framework of linear temporary market impact. Quantitative Finance, Vol: 21, Pages: 143-163
  43. ^ Damiano Brigo, Federico Graceffa and Eyal Neuman (2022). Price impact on term structure, Quantitative Finance, 22:1, 171-195, DOI: 10.1080/14697688.2021.1983201
  44. ^ John Armstrong and Damiano Brigo (2019). Risk managing tail-risk seekers: VaR and expected shortfall vs S-shaped utility. Journal of Banking & Finance, Vol: 101, Pages: 122-135
  45. ^ John Armstrong and Damiano Brigo (2022). Coherent risk measures alone are ineffective in constraining portfolio losses. Journal of Banking & Finance, Vol. 140
  46. ^ The Banker, Bracken Column, May 1, 2018. Damiano Brigo and John Armstrong, Basel risk limits will not curb rogue traders, https://www.thebanker.com/Transactions-Technology/Trading/Basel-risk-limits-will-not-curb-rogue-traders
  47. ^ Anthony Bellotti, Damiano Brigo, Paolo Gambetti and Frederic Vrins (2021). Forecasting recovery rates on nonperforming loans with machine learning. International Journal of Forecasting, Vol: 37, Pages: 428-444
  48. ^ Chris Lamberton, Damiano Brigo and Dave Hoy (2017). Impact of Robotics, RPA and AI on the insurance industry: challenges and opportunities. Journal of Financial Perspectives, Volume 4, issue 1, pp. 8-20.
  49. ^ John Armstrong and Damiano Brigo (2018). Intrinsic stochastic differential equations as jets. Proceedings of the Royal Society A - Mathematical physical and engineering sciences, 474(2210), 28 pages. doi:10.1098/rspa.2017.0559.
  50. ^ Aurelien Alfonsi and Damiano Brigo (2005). New Families of Copulas Based on Periodic Functions, Communications in Statistics: Theory and Methods, Vol. 34, N. 7
  51. ^ Damiano Brigo, Jan-Frederik Mai, and Matthias Scherer (2016). Markov multi-variate survival indicators for default simulation as a new characterization of the Marshall Olkin law. Statistics and Probability Letters, No. 114, p. 60-66
  52. ^ Damiano Brigo, Monique Jeanblanc and Frederic Vrins (2020). SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions. Stochastic Processes and their Applications, Vol: 130, Pages: 3895-3919
  53. ^ John Armstrong, Damiano Brigo, Thomas Cass, Emilio Rossi Ferrucci (2022). Non-geometric rough paths on manifolds. Journal of the London Mathematical Society, Vol. 106, issue 2, pages 756-817
  54. ^ a b https://www.finextra.com/pressarticle/47158/imperial-colleges-damiano-brigo-to-lead-capco-institute.
  55. ^ a b c Interview and Profile published in Risk Magazine, The risk-free myth, March 2011 issue

Reply 28-JUN-2023

[edit]

  Edit request declined  

  • Per WP:NOR, WP:NPOV, WP:BLPSOURCES.
    • 65% of the references proposed to be used in this edit request were written by the subject himself. Adding this content would jeopardize the article's requirement that it maintain a neutral point of view.

 Spintendo  02:55, 29 June 2023 (UTC)[reply]

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