Rama CONT: Research interests

Stochastic analysis: pathwise methods in stochastic analysis, Functional Ito calculus.

Mathematical foundations of Machine Learning: neural networks, generative models.

Systemic Risk

Complex networks

Mathematical modeling in finance:

Pathwise methods in stochastic analysis: Ito-Follmer calculus, causal functional calculus, Functional Ito calculus, path-dependent PDEs

  1. R Cont: Functional Ito calculus and functional Kolmogorov equations, Lectures Notes of the Barcelona Summer School on Stochastic Analysis, Centro de Recerca de Matematica (July 2012), in: V Bally et al: Stochastic integration by parts and Functional Ito calculus, Birkhauser.
  2. R Cont, R Jin (2021) Fractional Ito calculus, Transactions of the American Mathematical Society, Ser. B 11, 727-761.
  3. R Cont, Purba Das (2023) Quadratic variation and quadratic roughness, Bernoulli, Vol. 29, No. 1 (Feb 2023), 496-522.
  4. H Chiu, R Cont (2022) Causal Functional Calculus. Transactions of the London Mathematical Society, Volume 9, No. 1 December 2022, 237-269.
  5. R Cont, P Das (2022) Quadratic variation along refining partitions: constructions and examples, Journal of Mathematical Analysis and Applications, Volume 512, 126173.
  6. R Cont, A Kalinin (2020) On the support of solutions of stochastic differential equations with path-dependent coefficients . Stochastic Processes and their Applications, Vol. 130, Issue 5, May 2020, Pages 2639-2674.
  7. R Cont, N Perkowski (2019) Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity, Transactions of the American Mathematical Society (Series B), Volume 6, 161-186.
  8. H Chiu, R Cont (2018) On pathwise quadratic variation for cadlag functions, Electronic Communications in Probability, Volume 23, paper no. 85.
  9. A Ananova, R Cont (2017) Pathwise integration with respect to paths of finite quadratic variation, Journal de Mathematiques Pures et Appliquees, Volume 107, No 6, June 2017, 737-757.
  10. R Cont, Yi Lu (2016) Weak approximations for martingale representations, Stochastic Processes and Applications, Vol 126.
  11. P Blacque-Florentin, R Cont (2015) Functional calculus and martingale representation formula for integer-valued measures.
  12. R Cont, D Fournié (2013) Functional Ito calculus and stochastic integral representation of martingales, Annals of Probability, Vol 41, No 1, 109-133.
  13. R Cont, D Fournié (2009) A functional extension of the Ito formula , Comptes Rendus Mathématiques de l'Académie des Sciences, Volume 348, Issues 1-2, Pages 57-61.
  14. R Cont, D Fournié: Change of variable formulas for non-anticipative functional on path space, Journal of Functional Analysis, 259 (2010) 1043–1072.
  15. Mimicking the marginals of a semimartingale, 2009. With: Amel BENTATA.
  16. A Bentata, R Cont: Forward equations for option prices in semimartingale models, Finance and Stochastics, Volume 19, No. 3, 617-651, July 2015.

Mathematical foundations of Machine Learning

  1. Rama Cont, Alain Rossier, Renyuan Xu (2022) Asymptotic analysis of Deep Residual Networks .
  2. Rama Cont, Alain Rossier, Renyuan Xu (2022) Convergence and Regularization Properties of Gradient Descent for Deep Residual Networks .
  3. R Cont, Mihai Cucuringu, Renyuan Xu, Chao Zhang (2021) Tail-GAN: Learning to Simulate Tail Risk Scenarios.
  4. A Cohen, R Cont, A Rossier, Renyuan Xu (2021) Scaling properties of deep residual networks, International Conference on Machine Learning (ICML 2021).

Systemic Risk

  1. R Cont, E Schaanning (2019) Monitoring indirect contagion, Journal of Banking and Finance, Volume 104, July 2019, Pages 85-102.
  2. R Cont, Eric Schaanning (2016) Fire sales, indirect contagion and systemic stress-testing.
  3. R Cont (2017) Central clearing and risk transformation, Financial Stability Review (Banque de France).
  4. R Cont, E. B. Santos and A Moussa: Network structure and systemic risk in banking systems.
    in: JP Fouque & J Langsam (eds.): Handbook of Systemic Risk, Cambridge University Press, 2013.
  5. R Cont, L Wagalath (2013) Running for the exit: short selling and endogenous correlation in financial markets. Mathematical Finance Vol 23, Issue 4, p. 718-741, October 2013.
  6. R Cont, A Minca (2014) Credit default swaps and systemic risk, Annals Of Operations Research,.
  7. R Cont, L Wagalath: Fire sale forensics: measuring endogenous risk. Mathematical Finance, Volume 26, Issue 4 (Oct. 2016) 835-866.
  8. R Cont, L Wagalath (2016) Institutional investors and the dependence structure of asset returns. Int. J. Theor. Appl. Finance, Volume 19 (March 2016), 1650010-1650047.
  9. H Amini, R Cont, A Minca: Resilience to contagion in financial networks, Mathematical finance, Volume 26, Issue 2, pages 329-365, April 2016.
  10. H Amini, R Cont, A Minca (2012) Stress testing the resilience of financial networks, International Journal of Theoretical and applied finance, Vol 15.
  11. Credit default swaps and financial stability, Financial Stability Review, No 14, 35-43, July 2010.

Limit order markets

  1. R Cont, M Mueller (2019) A stochastic partial differential equation model for limit order book dynamics.
  2. Sirignano, J and Cont, R (2019) Universal Features of Price Formation in Financial Markets: Perspectives From Deep Learning, Quantitative Finance Vol. 19, No. 9.
    Featured in RISK Magazine (March 2018): Neural network learns universal model for stock-price moves.
  3. R Cont, A de Larrard (2013) Price dynamics in a Markovian limit order book market, SIAM Journal for Financial Mathematics, Vol 4, No 1, 1-25, 2013.
  4. R Cont, A Kukanov (2017) Optimal order placement in limit order markets, Quantitative Finance, Volume 17, No. 1, 21-39.
  5. A stochastic model for order book dynamics, Operations Research, Volume 58, 549-563, 2010. With: S Stoikov and R Talreja.
  6. Statistical Modeling of High Frequency Financial Data: Facts, Models and Challenges, IEEE Signal Processing, Volume 28.
  7. Order book dynamics in liquid markets: heavy traffic limits and jump-diffusion approximations, 2010. With: Adrien de LARRARD.
  8. Price dynamics in limit order markets: linking volatility with order flow, 2011. With: Adrien de LARRARD.
  9. R Cont, A Kukanov, S Stoikov (2014) The price impact of order book events, Journal of Financial Econometrics Vol 12, No 1, 47-88.

Credit Risk modeling

  1. Statistical Modeling of Credit default swap portfolios, 2011. With: YuHang KAN.
  2. Recovering Portfolio Default Intensities Implied by CDO Quotes, 2008. With: Andreea MINCA. To appear in: Mathematical Finance (2011).
  3. Dynamic hedging of portfolio credit derivatives. SIAM Journal of Financial Mathematics, Vol 2 (2011), 112-140. With : Yu Hang KAN.
  4. Credit default swaps and financial stability, Financial Stability Review (Banque de France), No 14, 35-43, July 2010.
  5. Default Intensities implied by CDO Spreads: Inversion Formula and Model Calibration, SIAM Journal of Financial Mathematics, Volume 1, pp. 555-585 (2010). With: R Deguest and Yu Hang KAN.
  6. Constant Proportion Debt Obligations (CPDO): Modeling and Risk Analysis, 2009. To appear in: Quantitative Finance. With: Cathrine Jessen.
  7. Forward equations for portfolio credit derivatives, published in: Chapter 11, R Cont (ed.): Frontiers in Quantitative Finance: credit risk and volatility modeling, Wiley, 2008. With: Ioana SAVESCU.
  8. R Cont (ed.) : Frontiers in Quantitative Finance: credit risk and volatility modeling, Wiley, 2008.
  9. R Bruyere, R Cont, R Copinot, C Jaeck, L Fery, T Spitz: Credit Derivatives, Wiley, 2005.

Computational finance: Option pricing and model calibration

  1. R Cont, R Deguest (2013) Equity correlations implied by index options: estimation and model uncertainty analysis, Mathematical Finance, Vol. 23, No. 3 (July 2013), 496--530.
  2. Recovering Portfolio Default Intensities Implied by CDO Quotes, 2008. With: Andreea MINCA. To appear in: Mathematical Finance (2011).
  3. A reduced basis method for option pricing, SIAM Journal of Financial Mathematics, Vol 2 (2011), 287-316. With: N Lantos and Olivier Pironneau.
  4. Default Intensities implied by CDO Spreads: Inversion Formula and Model Calibration, SIAM Journal of Financial Mathematics, Volume 1, pp. 555-585 (2010). With: R Deguest and Yu Hang KAN.
  5. Finite difference methods for option pricing in jump-diffusion and exponential Levy models. SIAM Journal of Numerical Analysis (2006), Vol 43, No. 4,� pp. 1596-1626. With: E Voltchkova.
  6. Recovering volatility from option prices by evolutionary optimization. Journal of Computational Finance (2005), Volume 8, No 3. With: S Ben Hamida.
  7. Retrieving L�vy processes from option prices: regularization of a nonlinear inverse problem. SIAM Journal of Control and Optimization, 45, 1, p 1-25 (2005). With: P Tankov.
  8. Nonparametric calibration of jump-diffusion processes,� Journal of Computational Finance (2004), Vol .7, No 3, pp 1-49. With: P Tankov.
  9. R Cont & P Tankov: Financial modelling with jump processes, Chapman and Hall/ CRC Press, 2003

Complex networks

  1. R Cont, E. B. Santos and A Moussa: Network structure and systemic risk in banking systems.
    in: JP Fouque & J Langsam (eds.): Handbook of Systemic Risk, Cambridge University Press, 2013.
  2. R Cont, Th Kokholm (2014) Central Clearing of OTC Derivatives: bilateral vs multilateral netting, Statistics and Risk Modeling, Vol 31, No. 1, 3-22, March 2014.
  3. H Amini, R Cont, A Minca: Stress testing the resilience of financial networks, International Journal of Theoretical and applied finance, Vol 15, (2012).
  4. H Amini, R Cont, A Minca: Resilience to contagion in financial networks, Mathematical finance, Volume 26, Issue 2, pages 329--365, April 2016.

Financial Modeling with Jump processes: Levy processes and integro-differential equations

  1. R Cont & P Tankov: Financial modelling with jump processes, Chapman and Hall/ CRC Press, 2003.
  2. R Cont, Th Kokholm: A Consistent Pricing Model for Index Options and Volatility Derivatives, Mathematical Finance, Vol 23, Issue 2, pages 248-274, April 2013.
  3. A Bentata, R Cont (2015) Forward equations for option prices in semimartingale models, Finance & Stochastics.July 2015, Volume 19, Issue 3, pp 617–65.
  4. Constant Proportion Portfolio Insurance in presence of jumps in asset prices, Mathematical Finance, Vol. 19, Issue 3, pp. 379-401, July 2009. With: P Tankov.
  5. Hedging with options in presence of jumps, in : Benth, F.E.; Di Nunno, G.; Lindstrom, T.; Oksendal, B.; Zhang, T. (Eds.) Stochastic Analysis and Applications: The Abel Symposium 2005 in honor of Kiyosi Ito, Springer 2007, pages 197-218. With: P Tankov, E Voltchkova.
  6. Finite difference methods for option pricing in jump-diffusion and exponential Levy models. SIAM Journal of Numerical Analysis (2006), Vol 43, No. 4, pp. 1596-1626. With: E Voltchkova.
  7. Integrodifferential equations for option prices in exponential Levy models, Finance & Stochastics, Volume 9, Number 3, pages 299-325 (2005). With: E Voltchkova.
  8. Nonparametric calibration of jump-diffusion processes, Journal of Computational Finance, Vol .7, No 3, pp 1-49. With: P Tankov.
  9. Option pricing models with jumps: integrodifferential equations and inverse problems. in: P Neittanmaki et al (Eds.): ECCOMAS 2004. With: E Voltchkova, P Tankov.
  10. Scaling in stock market data: stable laws and beyond, in: B. Dubrulle, F. Graner, D. Sornette (Eds.):Scale invariance and beyond, Springer, 1997.

Quantitative risk management

  1. R Cont, R Deguest, XueDong He (2013) Loss-based risk measures, Statistics and Decisions, Vol 30, May 2013.
  2. Central Clearing of interest rate swaps: a comparison of offerings, 2011. With: YuHua YU and Radu MONDESCU.
  3. Dynamic hedging of portfolio credit derivatives. SIAM Journal for Financial Mathematics, Vol 2 (2011), 112-140. With : Yu Hang KAN.
  4. Robustness and Sensitivity Analysis of Risk Measurement Procedures, Quantitative Finance, Vol. 10, No. 6, June–July 2010, 593–606 . With: R Deguest and G Scandolo.
  5. Model uncertainty and its impact on derivative instruments. Mathematical Finance, Vol 16, 519-542,� July 2006.

Statistical Modeling of Financial Data

  1. Statistical Modeling of Credit default swap portfolios, 2011. With: YuHang KAN.
  2. Nonparametric tests for the pathwise properties of semimartingales, Bernoulli, Vol 17, No 2, 781-813 (2011). With: Cecilia Mancini.
  3. Robustness and Sensitivity Analysis of Risk Measurement Procedures, Quantitative Finance, Vol. 10, No. 6, June–July 2010, 593–606 . With: R Deguest and G Scandolo.
  4. Modeling term structure dynamics: an infinite dimensional approach,� International Journal of Theoretical and Applied Finance, Vol 8, No 3, p 1-24 (2005).
  5. Long range dependence in financial time series, in:� Fractals in Engineering,� E Lutton & J Levy Vehel (Eds.), Springer (2005).
  6. Volatility clustering in financial markets, in:� A Kirman & G Teyssiere (Eds.): Long memory in economics,� Springer (2007), 289-310.
  7. Stochastic models of implied volatility surfaces, Economic Notes, vol. 31, No. 2, 361 - 377 (2002). With: Jose da Fonseca & Valdo Durrleman.
  8. Dynamics of implied volatility surfaces, �Quantitative Finance, Vol 2, No 2, ( 2002 ) 45-60. With: Jose da Fonseca.
  9. Empirical properties of asset returns: stylized facts and statistical issues, in: Quantitative Finance, Vol 1, No 2, (March 2001) 223-236.
  10. Phenomenology of the interest rate curve: a statistical analysis of term structure deformations, Applied Mathematical Finance, Vol. 6, No. 3 (Sept 1999).� With: JP Bouchaud, N ElKaroui, N Sagna, M Potters.
  11. Scaling in stock market data: stable laws and beyond, in: B. Dubrulle, F. Graner, D. Sornette (Eds.):Scale invariance and beyond, Springer, 1997.
  12. Are financial crashes predictable?, Europhysics Letters, Vol. 45, No. 1, pp. 1-5 (1999). With: JP Bouchaud, M Potters and L Laloux.

Endogenous risk: agent-based models and nonlinear dynamics in economics

  1. R Cont, L Wagalath (2013) Running for the exit: short selling and endogenous correlation in financial markets. Mathematical Finance Vol 23, Issue 4, p. 718-741, October 2013.
  2. Social distance, heterogeneity and social interactions. Journal of Mathematical Economics, Volume 46, 572-590, 2010. With: Matthias L�we.
  3. Heterogeneity and feedback in an agent-based market model, Journal of Physics: Condens. Matter 17 (2005) S1259-S1268. With: F Ghoulmie and JP Nadal.
  4. Volatility clustering in financial markets, in:� A Kirman & G Teyssiere (Eds.): Long memory in economics,� Springer (2007), 289-310.
  5. Modeling economic randomness: statistical mechanics of market phenomena, in: M Batchelor, L Wille (Eds.): Statistical Physics in the 21st century, World Scientific: 1998.
  6. "A Langevin approach to stock market fluctuations and crashes", European Physical Journal B 6 (1998) 4, 543-550.
  7. Herd behavior and aggregate fluctuations in speculative markets, Macroeconomic dynamics, Vol. 4, No.2, June 2000 (With: J.P. Bouchaud).

Mathematical finance: other topics

  1. Model-free representation of pricing rules as conditional expectations, in: Stochastic processes and applications to mathematical finance, Proceedings of the 6th Ritsumeikan International Symposium, World Scientific (2007), p 53-66. With: Sara Biagini.

Articles non-techniques en francais (in French)

  1. Benoit Mandelbrot et la mod�lisation math�matique en finance, Gazette des Math�maticiens No 136, 159-166 (April 2013).
  2. La mod�lisation math�matique des risques financiers (in French) Pour La Science , Dec 2008, p 24-27.
  3. Les statistiques face aux �v�nements extremes (in French) Pour La Science , Dec 2009, 24-27.
  4. La notation de credit des produits structures (in French) Echanges , Dec 2008, 69-72.

Miscellaneous

  1. Convergent multiplicative processes repelled from zero: power laws and truncated power laws, Journal de Physique I , Vol. 7, March 1997, 431-444 (with D. Sornette).