Damiano Brigo - Knowledge

338:

collateralization may not protect enough from losses, especially under default contagion, thus anticipating the discussion on initial margins. Brigo and co-authors were also among the first to introduce rigorously the debit valuation adjustment (DVA), while a volume on the updated nonlinear theory of valuation, including credit effects, collateral modeling and funding costs, has appeared in Brigo, Morini and Pallavicini (2013), a volume that also collects investigation of wrong way risk across asset classes and collects earlier research of the authors on collateral modeling and funding costs. Still on wrong way risk, Brigo and Vrins (2018) resort to a change of probability measure as a possible explanatory and computational technique. The research in this area expanded with several articles that contributed to give full mathematical rigor to the theory of credit and funding valuation adjustments, and to show their limits, highlighting the need for a full nonlinear valuation framework. These works include Brigo and Pallavicini (2014), who highlight the necessity of initial margin and the inherent nonlinear nature of the valuation problem under credit, collateral and funding effects, sketching the derivation of a valuation equation using advanced mathematical tools that will be made fully rigorous in subsequent papers. This research continued with Brigo, Buescu, and Rutkowski (2017), reconciling credit and funding effects with a basic option pricing theory, Brigo, Francischello and Pallavicini (2019) for a fully rigorous analysis of valuation as a fully nonlinear problem expressed mathematically through

141:. Brigo has been the most cited author for the technical section of Risk Magazine in the twenty years periods 1998–2017, and his research on credit-default-swaps (CDS)-calibration has been referenced in legal proceedings. More in detail, in 2011 the court of law in Novara, Italy, retried a case of financial intermediation after the bankruptcy of Lehman. The judgement explanation refers to Brigo's research article on credit calibration, which was an early online preprint version of Brigo, Morini and Tarenghi (2011), using their first passage firm-value models AT1P and SBTV to calibrate Lehman's CDS data, following an earlier application to Parmalat data. The court sentence states that "... in a recent study two different mathematical models (AT1P and SBTV) have been applied to the CDS trend of Lehman, and this shows that, despite a worsening of the estimate, even from a mathematical point of view, based on the CDS patterns, the survival probability of Lehman, even near the default event, was still high." 125:(2010-2012), where he headed the financial mathematics group. In 2012 Brigo moved to a full professor position at the Department of Mathematics of Imperial College London, where he headed the group in 2012-2019 and where he still serves as chair in mathematical finance, while continuing advisory work in the financial industry, serving in the academic advisory board of several financial institutions, and as director of two industry research institutes in two subsequent periods in 2012–2017, being often invited as a speaker both at academic events and at events organized by the industry, with seminars, talks, lectures, panels and training courses for international conferences, universities, mathematical institutes, financial institutions, central banks and regulators. 121:. After his PhD, Brigo pursued a career in the financial industry with several subsequent roles, first as a quantitative analyst in Banca Intesa in Milan, then as head of credit models in Banca IMI in London, and finally as a managing director with Fitch Ratings in London. While in the industry, Brigo had been appointed as external fixed income professor at Bocconi University and as a visiting professor at the Department of Mathematics at Imperial College London. By then a well known researcher and manager in the financial industry, Brigo moved to a full time academic career, starting with the Gilbart Chair full professorship in Financial Mathematics at 278:(2002) and Brigo, Mercurio and Sartorelli (2003), among others, and in a multivariate setting, allowing for reconciling single assets and index volatility smiles or triangulation of FX rates smiles, in Brigo, Rapisarda and Sridi (2018) and Brigo, Pisani and Rapisarda (2021). These mixture dynamics models have been successfully applied to different asset classes, see the specific 360:

in optimal trade execution, Bellani and Brigo (2022) show how one can do optimal execution in a model agnostic way, introducing the notion of good execution. Still in the context of optimal execution but with probability theory fully back in the framework, Brigo, Graceffa and Neumann (2022) show how to combine the theories of

432:

Still in the context of the theory of SDEs but without geometry, Brigo and co-authors worked on the theory of specific stochastic processes known as Peacocks in Brigo, Jeanblanc and Vrins (2020), linking them with Stochastic Differential Equations whose solutions are uniformly distributed. These SDEs

359:

techniques. This approach originated from an early result of Brigo and Mercurio (2000), where it is established that given an arbitrarily fine pre-assigned trading time grid, two statistically indistinguishable models in the grid can generate arbitrarily different options prices. For pathwise finance

323:

by Brigo, Pallavicini and Torresetti (2010), where, besides the dynamic loss models, the authors show research published before the crisis in 2006, highlighting the problems of the implied and base correlation paradigms that were dominating the valuation of credit index tranches at the time, based on

630:

Brigo, D., Morini, M. and Tarenghi, M. (2011). Credit calibration with structural models and equity return swap valuation under counterparty risk. In: Bielecki, Brigo and Patras (Editors), Credit Risk Frontiers: Subprime crisis, Pricing and Hedging, CVA, MBS, Ratings and Liquidity, Wiley/Bloomberg

372:

In the research area of risk management and risk measures in particular, Armstrong and Brigo (2019, 2022) 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

311:. Brigo focused also on multiname credit derivatives, showing in Brigo, Pallavicini and Torresetti (2007), through a dynamic loss model, how data implied a non-negligible probability that several names defaulted together, showing some large default clusters and a concrete risk of high losses in 302:

in particular, both for single name default options in Brigo (2005), Brigo and Alfonsi (2005), Brigo and El-Bachir (2010), and for credit default index options in Brigo and Morini (2011), showing how one could properly include a systemic default event in the valuation and clarifying the role of

414:

Brigo has been researching several areas of probability theory and statistics. His main work concerns the interaction of stochastic differential equations (SDEs) with the geometry of manifolds. Initially, this research has been applied to filtering, although later on, with the help of several

337:

for CVA, see for example Brigo and Pallavicini (2007), and later on Brigo, Capponi and Pallavicini (2014) for the case of wrong way risk with credit default swaps, where the underlying itself is default risky and default correlation plays a key role, highlighting the issue that even daily

332:

Brigo worked extensively on the theory and practice of valuation adjustments with several co-authors, being among the first in introducing early counterparty risk pricing calculations (later called credit valuation adjustment - CVA) in Brigo and Masetti (2006), and then focusing early on

354:

Brigo and co-authors further approached mathematical finance in general from a pathwise point of view, trying to establish results independently of the probabilistic setting. Armstrong, Bellani, Brigo and Cass (2021) show how to obtain option prices without probability theory, using

245:

Brigo and co-authors published several research papers on interest rate modeling, culminating in the monograph Brigo and Mercurio (2006) where the theory and practice of interest rate modelling are developed, including inflation modeling, credit risk modeling, early treatment of

1268:

Rehan Syed, Suriadi Suriadi, Michael Adams, Wasana Bandara, Sander J.J. Leemans, Chun Ouyang, Arthur H.M. ter Hofstede, Inge van de Weerd, Moe Thandar Wynn, Hajo A. Reijers (2020). Robotic Process Automation: Contemporary themes and challenges. Computers in Industry. Vol. 115,

415:

co-authors, it has been studied in its own right and has been applied to finance too. One of the main results is the interpretation of Ito SDEs as 2-jets. This interpretation is related to Schwartz morphism and was developed in Armstrong and Brigo (2018) via the structure of

58:, where he has been the most cited author in the twenty years 1998–2017. He is often requested as a plenary or invited speaker both at academic and industry international events. Brigo's research has also been used in court as support for legal proceedings. 54:, where he headed the Mathematical Finance group in 2012–2019. He is also a well known quantitative finance researcher, manager and advisor in the industry. His research has been cited and published also in mainstream industry publications, including 1085:

Tomasz R. Bielecki, Areski Cousin, Stéphane Crépey and Alexander Herbertsson (2014). A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries. Communications in Statistics - Theory and Methods 43(7), doi:

324:

the Gaussian copula, including the impossibility to match specific tranche spread patterns and the issue of allowing for negative expected tranched losses that pointed at possible arbitrage, see for example Torresetti, Brigo and Pallavicini (2006).

1254:

Marta Ramos González, Antonio Partal Ureña, Pilar Gómez Fernández-Aguado. (2023). Forecasting for regulatory credit loss derived from the COVID-19 pandemic: A machine learning approach. Research in International Business and Finance, Vol. 64,

423:

based on the Ito-vector and Ito-jet projections. In a similar vein, and with rough differential equations in mind, the study of non-geometric rough paths on manifolds has been approached in Armstrong, Brigo, Cass and Rossi Ferrucci (2022).

419:, with applications to filtering for both ordinary and quantum systems. Indeed, this work has inspired the optimal approximation of SDEs on submanifolds in Armstrong, Brigo and Rossi Ferrucci (2021) with applications leading to the 346:, and Brigo, Buescu, Francischello, Pallavicini and Rutkowski (2022) to reconcile the mathematically rigorous results on nonlinear valuation and valuation adjustments based on cash flows adjustments with an approach based on hedging. 641:

Brigo, D., and Pallavicini, A. (2014). Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks. International Journal of Financial Engineering 1 (01),

634:

Brigo, D., Capponi, A., and Pallavicini, A. (2014). Arbitrage-free bilateral counterparty risk valuation under collateralization and application to Credit Default Swaps. Mathematical Finance, Vol. 24, No. 1, pages 125–146.

737:

Brigo, D, Mai, J.F., and Scherer, M. (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.

669:

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:

1154:

Jin Liang and Hongchun Zou (2020). Valuation of credit contingent interest rate swap with credit rating migration. International Journal of Computer Mathematics. 97(12), pages 2546-2560, doi: 10.1080/00207160.2020.1713315

744:

Armstrong, J and Brigo, D. (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.

747:

Brigo, D., Jeanblanc, M. and Vrins, F. (2020). SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions. Stochastic Processes and their Applications, Vol: 130, Pages: 3895–3919.

307:, a form of credit default swaps where the premium leg does not pay a fixed and pre-agreed amount but a floating spread from a reference vanilla CDS over a constant time to maturity, see Brigo (2006) and the related 654:

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

754:

Armstrong, J, Brigo, D, and Rossi Ferrucci, E. (2021), Optimal approximation of SDEs on submanifolds: the Ito-vector and Ito-jet projections, Proceedings of the London Mathematical Society 119(1), pages 176–213,

682:

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,

600:

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,

236:

Mathematical finance is the research area where Brigo has been most active and is most known, both in academia and industry, authoring three monographs and about one hundred academic and industry publications.

441:

In probability and statistics, and in the theory of statistical distributions in particular, Alfonsi and Brigo (2005) have introduced new families of multivariate distributions through the concept of periodic

651:

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.

128:

Both during his run in the industry and his current work in academia, Brigo has been publishing academic and industry research that helped career progress. His joint monograph on interest rate models with

648:

Brigo, D., Buescu, C., and Rutkowski, M. (2017). Funding, repo and credit inclusive valuation as modified option pricing. OPERATIONS RESEARCH LETTERS, 45(6), pages 665–670. doi:10.1016/j.orl.2017.10.009

610:

Brigo, D., Pallavicini, A. (2007). Counterparty Risk under Correlation between Default and Interest Rates. In: Miller, J., Edelman, D., and Appleby, J. (Editors), Numerical Methods for Finance, Chapman

555:

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.

657:

Brigo, D., and Vrins, Frederic (2018). Disentangling wrong-way risk: pricing credit valuation adjustment via change of measures. European Journal of Operational Research 269(3), Pages 1154–1164,

992:

Skovmand D. and Verhofen, M. (2007). Book Review. Interest Rate Models - Theory and Practice, 2nd edition, Springer 2006. Fin Mkts Portfolio Mgmt (2007) 21:135–137, DOI 10.1007/s11408-006-0038-y

446:. Brigo, Mai and Scherer (2016) propose a new characterization of the Marshall-Olkin distribution. This is based on survival indicators of a related Markov chain and is applied to credit risk. 196:(besides the initial references, see in particular Armstrong and Brigo (2016), and Armstrong, Brigo and Rossi Ferrucci (2021)). Projection filters have been applied to several areas, including 1217:

Luciano Campi (2004). Arbitrage and completeness in financial markets with given N-dimensional distributions. Decisions in Economics and Finance 27, pages 57-80, doi: 10.1007/s10203-004-0044-3

567:

Brigo, D, Mercurio, F. (2002). Lognormal-mixture dynamics and calibration to market volatility smiles, International Journal of Theoretical and Applied Finance, 2002, Vol: 5, Pages: 427 - 446

523:

Armstrong, J, and Brigo, D. (2016). Nonlinear filtering via stochastic PDE projection on mixture manifolds in L2 direct metric, Mathematics of Control, Signals and Systems 28(1), Pages: 1-33.

1116:

Galina Andreeva, Jake Ansell and Tina Harrison (2014). Governance and Accountability of Public Risk. Financial Accountability and Management 30(3), pages 342-361, doi: 10.1111/faam.12036

676:

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,

1145:, Alessandro Gnoatto, and Immacolata Oliva (2021). A Unified Approach to xVA with CSA Discounting and Initial Margin. SIAM Journal on Financial Mathematics 12(3), doi 10.1137/20M1332153 663:

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,

761:

Armstrong, J, Brigo, D, Cass, T and Rossi Ferrucci, E. (2022). Non-geometric rough paths on manifolds. Journal of the London Mathematical Society, Vol. 106, issue 2, pages 756–817,

1296:

Yoshioka, H. (2020). Two-species competing population dynamics with the population-dependent environmental capacities under random disturbance. Theory Biosci. 139, pages 279–297.

397:

are examined in Bellotti, Brigo, Gambetti and Vrins (2021) who approach prediction of recovery rates with machine learning. In insurance, Lamberton, Brigo and Hoy (2017) show how

181: 496:

Brigo, D, Hanzon, B, LeGland, F. (1998). A differential geometric approach to nonlinear filtering: The projection filter, IEEE T AUTOMAT CONTR, 1998, Vol: 43, Pages: 247 - 252,

627:

Brigo, D and Morini, M. (2011). No-Armageddon Arbitrage-free Equivalent Measure for Index options in a credit crisis. Mathematical Finance, Vol. 21, Issue 4, pp. 573–593.

621:

Brigo, D, El-Bachir, N. (2010). An exact formula for default swaptions pricing in the SSRJD stochastic intensity model, Mathematical Finance, July 2010, pp. 365–382,

583:

Brigo, D, Alfonsi, A. (2005). Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model, FINANC STOCH, 2005, Vol: 9, Pages: 29 - 42,

157:

with Bernard Hanzon and Francois Le Gland, published mainly in Brigo, Hanzon and Le Gland (1998, 1999). This initial version of projection filters was investigated by the

506:

Brigo, D, Hanzon, B, Le Gland, F. (1999). Approximate nonlinear filtering by projection on exponential manifolds of densities, BERNOULLI, 1999, Vol: 5, Pages: 495 - 534,

561:

Brigo, D. and Mercurio, F. (2001). A deterministic–shift extension of analytically–tractable and time–homogeneous short–rate models. Finance and Stochastics 5, 369–387.

673:

Bellani, C. and Brigo, D. (2020). Mechanics of good trade execution in the framework of linear temporary market impact. Quantitative Finance, Vol: 21, Pages: 143-163

106: 695:

John Armstrong and Damiano Brigo (2022). Coherent risk measures alone are ineffective in constraining portfolio losses. Journal of Banking & Finance, Vol. 140.

137:

and has been widely adopted by academics and practitioners, the 2001 first edition being already considered a standard reference by reviewers. Brigo also authored

1205:

Andrew L. Allan, Chong Liu, David J. Prömel (2023). A Càdlàg Rough Path Foundation for Robust Finance. To appear in Finance and Stochastics, preprint available at

615: 701:

Brigo, D., Buescu, C., Francischello, M., Pallavicini, A. and Rutkowski, M. (2022). Nonlinear Valuation with XVAs: Two Converging Approaches. Mathematics 10(5),

539:

Brigo, D, Mercurio, F. (2006). Interest Rate Models: Theory and Practice - with Smile, Inflation and Credit, Heidelberg, Springer Verlag, 2001, 2nd Edition 2006.

707:

Brigo, D., Graceffa, F. and Neuman, E. (2022). Price impact on term structure. Quantitative Finance, 22(1), pages 171–195, doi: 10.1080/14697688.2021.1983201

542:

Brigo, D, Pallavicini, A, and Torresetti, R. (2010). Credit Models and the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Models. Wiley, 2010.

420: 689:

Brigo, D., Pisani, C. and Rapisarda, F. (2021). The multivariate mixture dynamics model: shifted dynamics and correlation skew. Ann Oper Res 299, 1411–1435.

1226:

Alimoradian, Behzad, Barigou, Karim and Eyraud-Loisel, Anne (2022). Derivatives under market impact: Disentangling cost and information. Available at SSRN:

1242:

Martin Herdegen and Nazem Khan (2021). Mean portfolio selection and rho-arbitrage for coherent risk measures. Mathematical Finance 32(1), pages 226-272,

545:

Brigo, D, Morini, M., and Pallavicini, A. (2013). Counterparty Credit Risk, Collateral and Funding, with Pricing Cases for All Asset Classes. Wiley, 2013.

1163:

Cont, R., & Kokholm, T. (2014). Central clearing of OTC derivatives: bilateral vs multilateral netting. Statistics & Risk Modeling, 31(1), 3-22.

717:

Brigo, D. (2000). On SDEs with marginal laws evolving in finite-dimensional exponential families, STAT PROBABIL LETT, 2000, Vol: 49, Pages: 127 - 134,

614:

Brigo, D, Pallavicini, A, Torresetti, R. (2007). Cluster-based extension of the generalized poisson loss dynamics andconsistency with single names,

1320:

Sloot, Henrik. "Implementing Markovian models for extendible Marshall–Olkin distributions" Dependence Modeling, vol. 10, no. 1, 2022, pp. 308-343.

570:

Brigo, D, Mercurio, F, Sartorelli, G. (2003). Alternative asset-price dynamics and volatility smile, QUANT FINANC, 2003, Vol: 3, Pages: 173 - 183,

173:. This work was part of Brigo's PhD studies, appearing in his PhD dissertation "Filtering by projection on the manifold of exponential densities". 1073:

Damien Ackerer, Damir Filipović (2019). Linear credit risk models. Finance and Stochastics, 24 (1), pages 169-214, doi 10.1007/s00780-019-00409-z

1002: 1436: 1196:

Berndsen, R. (2021). Fundamental questions on central counterparties: A review of the literature. Journal of Futures Markets, 41(12), 2009-2022.

361: 1184:

Antonelli, F., Ramponi, A. and Scarlatti, S. (2021). CVA and vulnerable options pricing by correlation expansions. Ann Oper Res 299, 401–427.

1446: 1441: 1466: 1461: 1411: 727:

Alfonsi, A, Brigo, D. (2005). New families of copulas based on periodic functions, COMMUN STAT-THEOR M, 2005, Vol: 34, Pages: 1437 - 1447,

885: 473: 254:

of models to market data. The monograph collects a good part of the earlier published research by the two authors and further co-authors.

604:

Torresetti, Brigo and Pallavicini (2006). Implied Correlation in CDO tranches: A Paradigm to be handled with care. SSRN working paper,

810: 192:

of probability densities. Brigo and co-authors considered different types of optimality criteria and metrics, leading to a variety of

1308:

Eckhard Liebscher (2008). Construction of asymmetric multivariate copulas. Journal of Multivariate Analysis 99(10), pages 2234-2250,

516:

Brigo, D. (1999). Diffusion Processes, Manifolds of Exponential Densities, and Nonlinear Filtering, In: Ole E. Barndorff-Nielsen and

339: 393:

In the area of machine learning and artificial intelligence applied to mathematical finance, and retail credit risk in particular,

177: 94: 308: 304: 46:, authoring more than 130 research publications and three monographs. From 2012 he serves as full professor with a chair in 1095:

Manuel Ammann, Mathis Moerke (2022). Credit variance risk premiums. European Financial Management, doi: 10.1111/eufm.12394

1456: 1125:

Cui, Q., & Ma, Y. (2014). Pricing synthetic CDO with MGB2 distribution. Statistics and Its Interface, 7(3), 309-318.

1019: 1172:

Glasserman, P., & Yang, L. (2018). Bounding Wrong‐Way Risk in CVA Calculation. Mathematical Finance, 28(1), 268-305.

526:

Armstrong, J, Brigo, D, and Hanzon, B. (2023). Optimal projection filters with information geometry. Info. Geo. (2023).

279: 271: 1061:

Musiela, M., and Rutkowski, M. (2004), Martingale Methods in Financial Modelling, 2nd Edition, Springer Verlag, Berlin.

711: 316: 267: 193: 114: 185: 1367: 312: 158: 433:

have to be analyzed with particular care as they have time-dependent non-Lipschitz and degenerate coefficients.

385:. The broad regulatory implications of this research were discussed in The Banker, Bracken Column, May 1, 2018. 1426: 1284:

Qing Gao, Guofeng Zhang, Ian R. Petersen (2020). An improved quantum projection filter. Automatica, Vol. 112,

1104:

Anlong Li (2006). Valuation of Swaps and Options on Constant Maturity CDS Spreads. Barclays Capital Research.

1416: 1340: 343: 102: 66: 247: 580:

Brigo, D. (2005). Market Models for CDS Options and Callable Floaters, Risk Magazine, January 2005 issue

1421: 1385: 936: 398: 593:

Brigo, D. (2006). Constant Maturity CDS valuation with market models. Risk Magazine, June 2006 issue.

1345: 788: 900: 225: 1354: 712:

Selected publications in stochastic analysis with differential geometry, probability and statistics

122: 1363: 876:

Has Basel got its numbers wrong? The Banker, Financial Times Group weekly magazine, June 21, 2011.

303:

information in the valuation. Brigo was also among the first to publish a method for valuation of

1395: 1376: 904: 848:

Campbell, Alexander (2011). The Risk-Free Myth. Risk Magazine 24(3), March 2011, London, page 80.

830: 51: 732: 722: 588: 575: 511: 501: 1431: 921: 401:

and artificial intelligence may be deployed to enhance performances in the insurance industry.

221: 1052:

Fengler, M. R. (2005), Semiparametric modeling of implied volatility, Springer Verlag, Berlin.

299: 166: 97:

under the supervision of Prof. Giovanni Battista Di Masi. Brigo continued his studies with a

35: 963: 294:

modeling and counterparty credit risk valuation. Brigo and co-authors worked extensively on

224:

and other areas, with the relevant references listed in the related projection filters page

1451: 404: 382: 321:

Credit Models and the Crisis: A journey into CDOs, Copulas, Correlations and Dynamic Models

170: 47: 23: 364:, related to optimal execution, with the theory of the term structure of interest rates. 8: 394: 295: 90: 74: 31: 1003:

Review of ``Interest Rate Models - Theory and Practice with smile, inflation and credit

378: 291: 150: 118: 39: 1142: 728: 718: 584: 571: 507: 497: 1285: 684: 636: 622: 517: 263: 162: 110: 27: 1382:

Video recording of the invited talk on stochastic differential equations as 2-jets

1372: 826: 888:, The Banker, Financial Times Group weekly magazine, Bracken Column, May 1, 2018. 696: 664: 443: 1336: 1270: 1349: 1126: 1032: 948: 792: 334: 275: 209: 205: 201: 134: 130: 65:

in stochastic nonlinear filtering with differential geometric methods from the

1391: 1381: 1256: 932: 1405: 1309: 1297: 1185: 690: 658: 527: 481:

Model risk in the transition to risk-free rates, Risk Magazine, June 5, 2018.

456: 374: 55: 749: 739: 643: 1231: 1392:

Video recording of the inaugural lecture on Randomness, Dynamics and Risk

1321: 605: 478:

Simple models won't cut it for systemic risk, Risk Magazine, May 8, 2018.

388: 381:

as risk measures are ineffective in curbing the potentially rogue trader

356: 349: 251: 217: 933:

Recording of invited talk on stochastic differential equations as 2-jets

556: 405:

Research on stochastic analysis and geometry, probability and statistics

367: 702: 469: 416: 197: 184:, evolving in an infinite dimensional space, with a finite dimensional 133:, Brigo and Mercurio (2006) has been cited more than 3000 times as per 43: 149:

Brigo started his research work with the development and study of the

144: 1243: 864:

Degrees of Influence, Risk Magazine, December 2018, pp. 129, Table B.

762: 756: 677: 562: 327: 1227: 468:

Basel risk limits will not curb rogue traders, with John Armstrong,

1206: 1105: 319:. This research has been updated in 2010, leading to the monograph 189: 188:

obtained via projection of the SPDE on a chosen finite dimensional

22:(born Venice, Italy 1966) is a mathematician known for research in 594: 520:, editor, Geometry in Present Day Science, World Scientific, 1999. 117:

in Amsterdam, with a dissertation that introduced and studied the

409: 549: 1027: 490: 86: 70: 533: 1358: 285: 213: 154: 105:, with periods under the supervision of Francois Le Gland at 98: 62: 436: 427: 139:

press columns and articles for The Banker and Risk Magazine

922:

King's College London impact case for mathematical finance

138: 93:, where he graduated cum laude with a dissertation on the 1037: 968: 616:

International Journal of Theoretical and Applied Finance

449: 101:

under the primary supervision of Bernard Hanzon at the

784: 782: 780: 778: 465:

Curbing rogue behaviour, Risk Magazine, April 9, 2018.

389:

Machine learning and RPA for credit risk and insurance

350:

Pathwise finance: option pricing and optimal execution

631:

Press, 457–484, 2011. DOI: 10.1002/9781118531839.ch14

368:

Risk measures and excessive tail-risk-seeking traders

860: 858: 856: 854: 1020:"Swedish Defense Research Agency Scientific Report" 775: 240: 231: 145:

Research on nonlinear filtering: projection filters

328:Valuation adjustments, XVA and nonlinear valuation 851: 1403: 1286:https://doi.org/10.1016/j.automatica.2019.108716 1138: 1136: 1134: 685:https://doi.org/10.1016/j.ijforecast.2020.06.009 637:https://doi.org/10.1111/j.1467-9965.2012.00520.x 623:https://doi.org/10.1111/j.1467-9965.2010.00401.x 462:XVA: back to CVA? Risk Magazine, March 20, 2018. 266:modelling, Brigo and co-authors have introduced 959: 957: 806: 804: 802: 800: 1280: 1278: 879: 822: 820: 818: 697:https://doi.org/10.1016/j.jbankfin.2021.106315 665:https://doi.org/10.1016/j.jbankfin.2019.01.010 410:Stochastic differential equations on manifolds 1271:https://doi.org/10.1016/j.compind.2019.103162 1131: 1012: 988: 986: 974: 903:at imperial.ac.uk, accessed on 20 July 2023, 886:Basel risk limits will not curb rogue traders 844: 842: 840: 838: 550:Selected publications in mathematical finance 455:Time to move on from risk-neutral valuation? 1180: 1178: 1127:https://dx.doi.org/10.4310/SII.2014.v7.n3.a1 1069: 1067: 954: 872: 870: 797: 491:Selected publications in nonlinear filtering 274:, both in a univariate setting in Brigo and 257: 1275: 1257:https://doi.org/10.1016/j.ribaf.2023.101907 1157: 1081: 1079: 815: 534:Selected monographs in mathematical finance 1310:https://doi.org/10.1016/j.jmva.2008.02.025 1298:https://doi.org/10.1007/s12064-020-00321-7 1186:https://doi.org/10.1007/s10479-019-03367-z 1166: 1106:Related 2006 SSRN Preprint available here. 1008:for the Mathematics Association of America 983: 964:Entry at the Mathematics Genealogy Project 835: 691:https://doi.org/10.1007/s10479-019-03239-6 659:https://doi.org/10.1016/j.ejor.2018.03.015 528:https://doi.org/10.1007/s41884-023-00108-x 340:backward stochastic differential equations 286:Credit derivatives and dynamic loss models 1175: 1064: 995: 977:Interest rate models: theory and practice 916: 914: 912: 867: 750:https://doi.org/10.1016/j.spa.2019.11.003 740:https://doi.org/10.1016/j.spl.2016.03.013 644:https://doi.org/10.1142/S2345768614500019 595:Related 2004 SSRN preprint available here 437:Probability and statistical distributions 428:SDEs with uniform distributions: peacocks 109:in Rennes, France, with the oversight of 1388:Risk and Stochastics Conference, London. 1076: 975:Brigo, Damiano; Mercurio, Fabio (2006). 939:Risk and Stochastics Conference, London. 485: 178:stochastic partial differential equation 169:approach to statistics, also related to 1098: 926: 80: 1404: 1322:https://doi.org/10.1515/demo-2022-0151 1232:http://dx.doi.org/10.2139/ssrn.4262080 909: 305:constant maturity credit default swaps 606:http://dx.doi.org/10.2139/ssrn.946755 557:https://doi.org/10.1007/s007800050009 450:Press columns in mathematical finance 290:From 2002, Brigo contributed also to 1447:Academics of Imperial College London 1442:Academic staff of Bocconi University 920:Research Excellence Framework 2014: 896: 894: 703:https://doi.org/10.3390/math10050791 50:at the Department of Mathematics of 1467:20th-century Italian mathematicians 1462:Vrije Universiteit Amsterdam alumni 1412:21st-century Italian mathematicians 421:latest family of projection filters 176:Projection filters approximate the 13: 1437:Academics of King's College London 1373:Damiano Brigo's institutional page 1244:https://doi.org/10.1111/mafi.12333 763:https://doi.org/10.1112/jlms.12585 757:https://doi.org/10.1112/plms.12226 678:https://doi.org/10.1111/mafi.12308 563:https://doi.org/10.1007/PL00013541 14: 1478: 1330: 1228:https://ssrn.com/abstract=4262080 891: 268:stochastic differential equations 216:diameters, estimation of chaotic 1207:https://arxiv.org/abs/2109.04225 241:Interest rate derivatives models 232:Research on mathematical finance 186:stochastic differential equation 1368:Social Science Research Network 1364:Damiano Brigo's research papers 1355:Damiano Brigo's research papers 1314: 1302: 1290: 1262: 1248: 1236: 1220: 1211: 1199: 1190: 1148: 1119: 1110: 1089: 1055: 1046: 949:University of Padua Alumni Page 942: 789:Publications and citations page 313:collateralized debt obligations 159:Swedish Defense Research Agency 73:degree in mathematics from the 979:. Heidelberg: Springer-Verlag. 344:partial differential equations 1: 1394:, held on 29 January 2014 at 1341:Mathematics Genealogy Project 768: 317:financial crisis of 2007–2008 161:. The projection filters are 89:degree in mathematics at the 1086:10.1080/03610926.2013.844251 474:Bracken Column, May 1, 2018. 248:credit valuation adjustments 103:Free University of Amsterdam 67:Free University of Amsterdam 7: 95:nonlinear filtering problem 10: 1483: 1457:University of Padua alumni 1386:London School of Economics 937:London School of Economics 399:robotic process automation 1346:Damiano Brigo's citations 270:that are consistent with 258:Volatility smile modeling 1384:, presented at the 2016 282:for further references. 272:dynamical mixture models 1396:Imperial College London 1377:Imperial College London 905:Imperial College London 831:Imperial College London 52:Imperial College London 300:credit default options 222:change point detection 180:(SPDE) of the optimal 167:differential geometric 1427:Probability theorists 1337:Damiano Brigo's Entry 486:Selected publications 123:King's College London 36:differential geometry 1417:Financial economists 935:, at 1 minute, 2016 395:non-performing loans 383:utility maximization 171:information geometry 85:Brigo studied for a 81:Education and career 48:mathematical finance 24:mathematical finance 518:Eva B. Vedel Jensen 296:credit default swap 91:University of Padua 75:University of Padua 32:stochastic analysis 1001:Donev, C. (2007). 901:Damiano Brigo's CV 827:Institutional page 379:expected shortfall 292:credit derivatives 194:projection filters 151:projection filters 119:projection filters 40:probability theory 1422:Control theorists 1143:Francesca Biagini 163:nonlinear filters 1474: 1324: 1318: 1312: 1306: 1300: 1294: 1288: 1282: 1273: 1266: 1260: 1252: 1246: 1240: 1234: 1224: 1218: 1215: 1209: 1203: 1197: 1194: 1188: 1182: 1173: 1170: 1164: 1161: 1155: 1152: 1146: 1140: 1129: 1123: 1117: 1114: 1108: 1102: 1096: 1093: 1087: 1083: 1074: 1071: 1062: 1059: 1053: 1050: 1044: 1043: 1041: 1031:. Archived from 1024: 1016: 1010: 999: 993: 990: 981: 980: 972: 966: 961: 952: 946: 940: 930: 924: 918: 907: 898: 889: 883: 877: 874: 865: 862: 849: 846: 833: 824: 813: 808: 795: 786: 342:and semi-linear 264:volatility smile 212:, estimation of 182:nonlinear filter 111:Jan van Schuppen 28:filtering theory 1482: 1481: 1477: 1476: 1475: 1473: 1472: 1471: 1402: 1401: 1333: 1328: 1327: 1319: 1315: 1307: 1303: 1295: 1291: 1283: 1276: 1267: 1263: 1253: 1249: 1241: 1237: 1225: 1221: 1216: 1212: 1204: 1200: 1195: 1191: 1183: 1176: 1171: 1167: 1162: 1158: 1153: 1149: 1141: 1132: 1124: 1120: 1115: 1111: 1103: 1099: 1094: 1090: 1084: 1077: 1072: 1065: 1060: 1056: 1051: 1047: 1035: 1022: 1018: 1017: 1013: 1000: 996: 991: 984: 973: 969: 962: 955: 947: 943: 931: 927: 919: 910: 899: 892: 884: 880: 875: 868: 863: 852: 847: 836: 825: 816: 809: 798: 787: 776: 771: 714: 552: 536: 493: 488: 452: 444:copula function 439: 430: 412: 407: 391: 370: 352: 330: 288: 260: 243: 234: 210:quantum systems 147: 83: 17: 12: 11: 5: 1480: 1470: 1469: 1464: 1459: 1454: 1449: 1444: 1439: 1434: 1429: 1424: 1419: 1414: 1400: 1399: 1389: 1379: 1370: 1361: 1352: 1350:Google Scholar 1343: 1332: 1331:External links 1329: 1326: 1325: 1313: 1301: 1289: 1274: 1261: 1247: 1235: 1219: 1210: 1198: 1189: 1174: 1165: 1156: 1147: 1130: 1118: 1109: 1097: 1088: 1075: 1063: 1054: 1045: 1042:on 2016-03-03. 1011: 994: 982: 967: 953: 941: 925: 908: 890: 878: 866: 850: 834: 814: 796: 793:Google Scholar 773: 772: 770: 767: 766: 765: 759: 752: 745: 742: 735: 725: 713: 710: 709: 708: 705: 699: 693: 687: 680: 674: 671: 667: 661: 655: 652: 649: 646: 639: 632: 628: 625: 619: 612: 608: 602: 598: 591: 581: 578: 568: 565: 559: 551: 548: 547: 546: 543: 540: 535: 532: 531: 530: 524: 521: 514: 504: 492: 489: 487: 484: 483: 482: 479: 476: 466: 463: 460: 459:, Feb 8, 2018. 451: 448: 438: 435: 429: 426: 411: 408: 406: 403: 390: 387: 369: 366: 351: 348: 335:wrong way risk 329: 326: 287: 284: 259: 256: 242: 239: 233: 230: 206:quantum optics 202:ocean dynamics 146: 143: 135:Google Scholar 131:Fabio Mercurio 82: 79: 69:, following a 61:Brigo holds a 15: 9: 6: 4: 3: 2: 1479: 1468: 1465: 1463: 1460: 1458: 1455: 1453: 1450: 1448: 1445: 1443: 1440: 1438: 1435: 1433: 1432:Living people 1430: 1428: 1425: 1423: 1420: 1418: 1415: 1413: 1410: 1409: 1407: 1397: 1393: 1390: 1387: 1383: 1380: 1378: 1374: 1371: 1369: 1365: 1362: 1360: 1356: 1353: 1351: 1347: 1344: 1342: 1338: 1335: 1334: 1323: 1317: 1311: 1305: 1299: 1293: 1287: 1281: 1279: 1272: 1265: 1258: 1251: 1245: 1239: 1233: 1229: 1223: 1214: 1208: 1202: 1193: 1187: 1181: 1179: 1169: 1160: 1151: 1144: 1139: 1137: 1135: 1128: 1122: 1113: 1107: 1101: 1092: 1082: 1080: 1070: 1068: 1058: 1049: 1039: 1034: 1030: 1029: 1021: 1015: 1009: 1006: 1005: 998: 989: 987: 978: 971: 965: 960: 958: 950: 945: 938: 934: 929: 923: 917: 915: 913: 906: 902: 897: 895: 887: 882: 873: 871: 861: 859: 857: 855: 845: 843: 841: 839: 832: 828: 823: 821: 819: 812: 811:Finextra news 807: 805: 803: 801: 794: 790: 785: 783: 781: 779: 774: 764: 760: 758: 753: 751: 746: 743: 741: 736: 734: 730: 726: 724: 720: 716: 715: 706: 704: 700: 698: 694: 692: 688: 686: 681: 679: 675: 672: 668: 666: 662: 660: 656: 653: 650: 647: 645: 640: 638: 633: 629: 626: 624: 620: 617: 613: 609: 607: 603: 599: 596: 592: 590: 586: 582: 579: 577: 573: 569: 566: 564: 560: 558: 554: 553: 544: 541: 538: 537: 529: 525: 522: 519: 515: 513: 509: 505: 503: 499: 495: 494: 480: 477: 475: 471: 467: 464: 461: 458: 457:Risk Magazine 454: 453: 447: 445: 434: 425: 422: 418: 402: 400: 396: 386: 384: 380: 376: 375:value at risk 365: 363: 358: 347: 345: 341: 336: 325: 322: 318: 315:prior to the 314: 310: 306: 301: 297: 293: 283: 281: 277: 273: 269: 265: 255: 253: 249: 238: 229: 227: 223: 219: 215: 211: 207: 203: 199: 195: 191: 187: 183: 179: 174: 172: 168: 165:based on the 164: 160: 156: 153:, during his 152: 142: 140: 136: 132: 126: 124: 120: 116: 112: 108: 104: 100: 96: 92: 88: 78: 76: 72: 68: 64: 59: 57: 56:Risk Magazine 53: 49: 45: 41: 37: 33: 29: 25: 21: 20:Damiano Brigo 16:Mathematician 1316: 1304: 1292: 1264: 1250: 1238: 1222: 1213: 1201: 1192: 1168: 1159: 1150: 1121: 1112: 1100: 1091: 1057: 1048: 1033:the original 1026: 1014: 1007: 1004: 997: 976: 970: 951:(in Italian) 944: 928: 881: 440: 431: 413: 392: 371: 362:price impact 353: 331: 320: 289: 261: 244: 235: 226:applications 175: 148: 127: 84: 60: 19: 18: 1452:1966 births 417:jet bundles 357:rough paths 252:calibration 218:time series 107:IRISA/INRIA 1406:Categories 769:References 470:The Banker 198:navigation 44:statistics 733:0361-0926 723:0167-7152 618:, Vol: 10 589:0949-2984 576:1469-7688 512:1350-7265 502:0018-9286 276:Mercurio 190:manifold 1339:at the 670:788-805 601:London. 1028:foi.se 731: 721: 587: 574: 510: 500: 87:laurea 71:laurea 1359:arXiv 1023:(PDF) 611:Hall. 309:entry 280:entry 214:fiber 155:Ph.D. 99:Ph.D. 63:Ph.D. 34:with 729:ISSN 719:ISSN 585:ISSN 572:ISSN 508:ISSN 498:ISSN 298:and 250:and 208:and 42:and 1375:at 1366:at 1357:at 1348:in 1230:or 1038:PDF 829:at 791:in 472:, 377:or 262:In 115:CWI 113:at 1408:: 1277:^ 1177:^ 1133:^ 1078:^ 1066:^ 1025:. 985:^ 956:^ 911:^ 893:^ 869:^ 853:^ 837:^ 817:^ 799:^ 777:^ 228:. 220:, 204:, 200:, 77:. 38:, 30:, 26:, 1398:. 1259:. 1040:) 1036:( 597:.

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.