Publications

Books

Books as Author

• Malliavin Calculus for Lévy Processes with Applications to Finance, Authors: Giulia Di Nunno, Bernt Øksendal, and Frank Proske. Springer, 2009. ISBN 9783540785712 (418 pages). See here

Books as Editor

• Computation and Combinatorics in Dynamics, Stochastics and Control. The Abel Symposium 2016. Editors: Elena Celledoni, Giulia Di Nunno, Kurusch Ebrahimi-Fard, and Hans Munthe-Kaas. Springer 2018. 738 pages. See here

• Stochastics for Environmental and Financial Economics. Editors: Fred Espen Benth and Giulia Di Nunno, Springer 2016. ISBN 978-3-319-23424-3. 362 pages in Open Access

• Advanced Mathematical Methods for Finance. Editors: Giulia Di Nunno and Bernt Øksendal. Springer, 2011.  ISBN 978-3-642-18411-6.  536 pages. See here

• Stochastic Analysis and Applications. The Abel Symposium 2005, Oslo, July 29 - August 4, 2005, held in honor of Kiyosi Itô. Editors: Fred Espen Benth, Giulia Di Nunno, Tom Lindstrøm, Bernt Øksendal, and Tusheng Zhang. Springer, 2007.  ISBN 9783540708469.  678 pages. See here

Editor of Special Numbers in Scientific Journals

• Frontiers in "Long-Memory Models in Mathematical Finance" (2021). Eds. E. Alòs, E. Azmoodeh, G. Di Nunno, T. Sottinen. Open access

• Stochastics, 89 (2017) 1. Special Issue: Festschrift for Bernt Øksendal. Eds. F.E. Benth, G. Di Nunno, and S. Jacka

• Stochastics, 84 (2012) 2-3. Special Issue: Stochastic Analysis and Applications. Eds. S. Albeverio, G. Di Nunno, B. Øksendal, and H. Ouerdiane. Proceedings of the Conference in Stochastic Analysis and Applications, October 12-17, 2009, Hammamet

• Stochastics, 84 (2012), 5-6. The Mark H.A. Davis festschrift: stochastics, control and finance. Eds. D. Becherer, G. Di Nunno, H. Zhang, and M. Zervos

• Stochastics, 81 (2009), 3-4: Special Issue: Stochastic Analysis. Eds. N. El Karoui, P. Malliavin, G. Di Nunno, N. Obata, B. Øksendal, and H. Ouerdiane. Proceedings of the Conference in Stochastic Analysis and Applications, November 5-10, 2007. Hammamet

Articles, Chapters, and Preprints

1. Cash non-additive risk measures: horizon risk and generalized entropy. Coauthor: Emanuela Rosazza Gianin (U. Milano Bicocca). arXiv:2401.14443

2. Power law in Sandwiched Volterra Volatility model. Coauthor: Anton Yurchenko-Tytarenko (UiO).  Modern Stoch. Theory Appl.(2024), 1-26, DOI 10.15559/24-VMSTA246

3. From constant to rough: A survey of continuous volatility modelling. Coauthors: Kestutis Kubilius (Vilnius University), Yulyia Mishura (Taras Shevchenko National University of Kyiv, Mælardalen University) and Anton Yurchenko-Tytarenko (UiO). Mathematics 2023, 11(19), 4201.  https://doi.org/10.3390/math11194201 

4. Lifting of Volterra processes: optimal control in UMD Banach spaces. Coauthor: Michele Giordano (UiO). arXiv:2306.14175

5. Fully-dynamic risk measures: horizon risk, time-consistency, and relations with BSDEs and BSVIEs. Coauthors: Emanuela Rosazza Gianin (U. Milano Bicocca). arXiv:2301.04971 Accepted in SIAM J. Financial Mathematics

6. Sandwiched Volterra Volatility model: Markovian approximations and hedging. Coauthors: Anton Yurchenko-Tytarenko (UiO). arXiv:2209.13054

7. Option pricing in Volterra sandwiched volatility model. Coauthors: Yulyia Mishura (Taras Shevchenko National University of Kyiv) and Anton Yurchenko-Tytarenko (UiO). arXiv:2209.10688 

8. Before and after default: information and optimal portfolio via anticipating calculus. Coauthors: Bernardo D'Auria (University of Padova)  and José A. Salmerón (University Carlos III Madrid), arXiv:2208.07163 

9. The heat modulated infinite dimensional Heston model and its numerical approximation. Coauthors: Gabriel Lord (Radbound Universtiy, Nijmegen)  and Fred Espen Benth and Andreas Petersson (UiO), arXiv:2206-10166

10. Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises. Coauthors: Yuliya Mishura (Taras Shevchenko National University of Kyiv) and Anton Yurchenko-Tytarenko (UiO). Numer. Algor., 2022 https://doi.org/10.1007/s11075-022-01424-6

11. On stochastic control for time changed Lévy dynamics. SeMa Journal 79, nr 3, 2022, pp. 529-547 https://doi.org/10.1007/s40324-022-00301-5

12. SPDE bridges with observation noise and their spatial approximation. Coauthors: Salvador Ortiz-Latorre and Andreas Petersson (UiO). Stochastic Processes and Applications, 158, 2023, 170-207 https://doi.org/10.1016/j.spa.2023.01.007

13. A topological proof of Sklar's theorem in arbitrary dimensions. Coauthors: Fred Espen Benth and Dennis Schroes (UiO). Dependence Modeling, vol. 10, no. 1, 2022, pp. 22-28. https://doi.org/10.1515/demo-2022-0103

14. Sensitivity analysis in the infinite dimensional Heston model. Coauthors: Fred Espen Benth and Iben C. Simonsen (UiO). IDA-QP Infin. Dimens. Anal. Quantum Probab. Relat. Top., 24(2), 2021, 2150015

15. Copula measures and Sklar's theorem in arbitrary dimensions. Coauthors: Fred Espen Benth and Dennis Schroes (UiO). Scandinavian Journal of Statistics, 2021. https://doi.org/10.1111/sjos.12559

16. Sandwiched SDEs with unbounded drift driven by Hölder noises. Coauthors: Yuliya Mishura (Taras Shevchenko National University of Kyiv) and Anton Yurchenko-Tytarenko (UiO). Advances in Applied Probability,55(3), 2023, 927-964. doi:10.1017/apr.2022.56

17. Maximum principles for stochastic time-changed Volterra games. Coauthor: Michele Giordano (UiO).arXiv:2012.06449 

18. Stochastic Volterra equations with time-changed Lévy noise and maximum principles. Coauthor: Michele Giordano (UiO). Ann Oper Res (2023). https://doi.org/10.1007/s10479-023-05303-8

19. Stochastic differential equations drivne by additive Volterra-Lévy and Volterra-Gaussian noises. Coauthors: Yuliya Mishura and Kostiantyn Ralchenko (Taras Shevchenko National University of Kyiv). Chapter 14 in "Stochastic Processes, Statistical Methods and Engineering Mathematics. Eds A. Malyarenko, Y. Ni, M. Rancic, and S. Silvestrov, Springer 2022.  https://link.springer.com/book/10.1007/978-3-031-17820-7

20. Path-dependent Kyle equilibrium model. Coauthor: Jose Manuel Corcuera (University of Barcelona). arXiv:2006.06395

21. Utility maximisation and time change. Coauthors: Hannes Haferkorn (Commerzbank), Asma Khedher (U. Amsterdam), Michèle Vanmaele (U. Ghent). arXiv:1912.03202 

22. On the approximation of Lévy driven Volterra processes and their integrals. Coauthors: Andrea Fiacco (University of Oslo), Erik H. Karlsen (IF Skadeforsikring). Journal of Mathematical Analysis and Applications, 2019. doi.org/10.1016/j.jmaa.2019.02.051

23. Kyle equilibrium under random price pressure. Coauthors: Jose Manuel Corcuera (University of Barcelona), José Fajardo (Brazilian School of Public and Business Administration). Decisions in Economics and Finance 42(1), 2019, 77-101.

24. Kyle-Back's model with a random horizon. Coauthor: Jose Manuel Corcuera (University of Barcelona). Int. J. Theor. Appl. Finan. 21, 1850016 (2018) doi.org/10.1142/S0219024918500164 

25. Fully-dynamic risk-indifference prices and no-good-deal bounds. Coauthor: Jocelyne Bion-Nadal (CNRS-Ecole Politechnique).SIAM Journal on Financial Mathematics 11(2), 2020, 620-658. doi.org/10.1137/18M120436X 

26. Stochastic functional differential equations and sensitivity to their initial path. Coauthors: David R. Banos, Hannes Haferkorn, and Frank Proske (UiO). In Computation and Combinatorics in Dynamics, Stochastics and Control. The Abel Symposium 2016. Editors: E. Celledoni, G. Di Nunno, K. Ebrahimi-Fard, and H. Munthe-Kaas.  

27. Fractional calculus and path wise integration for Volterra processes driven by Lévy and martingale noise. Coauthors: Yuliya Mishura and Kostiantyn Ralchenko (Taras Shevchenko National University of Kyiv). Fractional Calculus and Applied Analysis 19 (2016), no. 6, 1314-2224 doi.org/10.1515/fca-2016-0071

28. A maximum principle for mean-field SDEs with time change. Coauthors: Hannes Haferkorn (UiO). Applied Mathematics and Optimisation 76 (2017), no 1, 137-176.

29. Stochastic systems with memory and jumps. Coauthors: David R. Banos (UiO, Univ. Barcelona), Francesco Cordoni (Univ. Trento), Luca Di Persio (Univ. Verona), Elin E. Røse (UiO). Journal of Differential Equations.  Online November 2018  doi.org/10.1016/j.jde.2018.10.052

30. A Malliavin-Skorohod calculus in L^0 and L^1 for additive and Volterra-type processes. Coauthor: Josep Vives (University of Barcelona). Stochastics 89 (2017), no. 1, 142-170. 

31. Hedging under worst-case-scenario in a market driven by time-changed Lévy noises. Coauthor: Erik H. Karlsen (UiO). Chapter in "The fascination of Probability, Statistics and their Applications. In onour of Ole Barndorff-Nielsen on his 80th birthday" Springer 2016. Pages 465-499. Editors: M. Podolskij, R. Stelzer, S. Thorbjørsen, A. Veraart.

32. Representation of convex operators and their static and dynamic sandwich extensions. Coauthor: Jocelyne Bion-Nadal (CNRS - Ecole Polytechnique France). Journal of Convex Analysis 24 (2017), no. 4, 1375-1405.

33. Approximations of stochastic partial differential equations. Coauthor: Tusheng Zhang (University of Manchester). Annals of Applied Probability 26 (2016), no.3, 1443-1466.

34. Robustness of quadratic hedging strategies in finance via backward stochastic differential equations with jumps. Coauthors: Asma Khedher (Technical University Munich) and Michèle Vanmaele (University of Gent). Applied Mathematics and Optimisation, 72 (December 2015), 353 - 389.

35. BSDEs driven by time-changed Lévy noises and optimal control. Coauthor: Steffen Sjursen (University of Oslo) Stochastic Processes and their Applications, 124 (2014), 1679 -1709. 

36. Pricing of spread options on a bivariate jump market and stability to model risk. Coauthors: Fred Espen Benth, Asma Khedher, and Maren Diane Schmeck (University of Oslo). Applied Mathematical Finance, 22 (2015), 28-62

37. Information and optimal investment in defaultable assets. Coauthor: Steffen Sjursen (University of Oslo). International Journal of Theoretical and Applied Finance, 17 (2014), 1450050- (27 pages) 

38. On chaos representation and orthogonal polynomials for the doubly stochastic Poisson process. Coauthor: Steffen Sjursen (University of Oslo). Seminar on Stochastic Analysis, Random Fields and Applications VII. (Ascona, Switzerland, May 23- 27,2011). Eds. R.C. Dalang, M. Dozzi, F. Russo. Birkhäuser, Progress in Probability Vol. 67 (2013). Pages 23-54.

39. Dynamic no-good-deal pricing measures and extension theorems for linear operators on L∞.  and application to price systems. Coauthor: Jocelyne Bion-Nadal (CNRS - Ecole Polytechnique France). Finance and Stochastics, 17 (2013), 587-613 On line: August 2012. (Eprint with title: Extension theorems for linear operators on L∞ and application to price systems. ArXiv 1102.5501).

40. A note on convergence of option prices and their Greeks for Lévy models. Coauthors: Fred Espen Benth and Asma Khedher (University of Oslo). Stochastics, 85 (2013), 1015-1039.

41. Computation of Greeks in multi-factor models with applications to power and commodity markets. Coauthors: Fred Espen Benth, and Asma Khedher (University of Oslo). The Journal of Energy Markets (2012). 

42. Robustness of option prices and their deltas in markets modelled with jump-diffusions. Coauthors: Fred Espen Benth and Asma Khedher (University of Oslo). Comm. Stochastic Analysis 5 (2011), 285-307. 

43. A general maximum principle for anticipative stochastic control and applications to insider trading. Coauthors: Bernt Øksendal, Olivier Menoukeu Pamen, and Frank Proske (University of Oslo). Chapter 7 in Advanced Mathematical Methods for Finance, Springer, 2011. pp. 181-221.

44. Lévy models robustness and sensitivy. Coauthors: Fred Espen Benth and Asma Khedher (University of Oslo). Quantum Probability and Infinite dimensional Analysis. Volume XXV In the series in QP-PQ, Quantum Probability and White Noise Analysis. Eds. H. Ouerdiane and A. Barhoumi, World Scientific, 2010. Pages 153-184. 

45. Uniqueness of decompositions of Skorohod-semimartingales. Coauthors: Bernt Øksendal, Olivier Menoukeu Pamen, and Frank Proske (University of Oslo). Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14 (2011), 15-24. 

46. Lower and upper bounds of martingale measure densities in continuous time markets. Coauthor: Inga B. Eide (University of Oslo). Mathematical Finance 21 (2011), 475-492. On line:19 OCT 2010. 

47. Minimal variance hedging in large financial markets: random fields approach. Coauthor: Inga B. Eide (University of Oslo). Stochastic Analysis and Applications 28 (2010), 54-85. 

48. Optimal portfolio, partial information and Malliavin calculus. Coauthor: Bernt Øksendal (University of Oslo). Stochastics 81 (2009), 303-322.

49. Stochastic integrals and adjoint derivatives. Coauthor: Yuri A. Rozanov (CNR - Milano). Chapter 11 in Stochastic Analysis and its Applications. Springer, 2007. Pages 265-307.

50. A representation theorem and a sensitivity result for functionals of jump diffusions. Coauthor: Bernt Øksendal (University of Oslo). Chapter 15 in Mathematical Analysis of Random Phenomena, World Scientific, 2007. Pages 177-190. 

51. Random Fields: non-anticipating derivative and differentiation formulas. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10 (2007), 465-481. 

52. Anticipative stochastic control for Lévy processes with application to insider trading. Coauthors: Arturo Kohatzu-Higa (INRIA - Rocquencourt), Thilo Meyer Brandis, Bernt Øksendal, Frank Proske (University of Oslo), and Agnès Sulem (INRIA - Rocquencourt). Chapter 14 in Handbook in Mathematical Sciences.ELSEVIER, 2008. Pages 575-596. 

53. The Donsker delta function, a representation formula for functionals of a Lévy process and application to hedging in incomplete markets. Coauthor: Bernt Øksendal (University of Oslo). SMF Seminaires et Congres 16 (2007), 71-82.

54. On orthogonal polynomials and the Malliavin derivative for Lévy stochastic measures. SMF Seminaires et Congres 16 (2007), 55-69.

55. Optimal portfolio for an insider in a market driven with Lévy processes. Coauthors: Thilo Meyer-Brandis, Bernt Øksendal and Frank Proske (University of Oslo). Quantitative Finance 6 (2006), 83-94.

56. Price operators analysis in Lp-spaces. Coauthors: Sergio Albeverio (University of Bonn) and Yuri A. Rozanov (CNR-Milano). Acta Applicandae Mathematicae 89 (2005), 85-108.

57. Malliavin calculus and anticipative Itô formulae for Lévy processes. Coauthors: Thilo Meyer-Brandis, Bernt Øksendal, and Frank Proske (University of Oslo). Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 (2005), 235-258.

58. White noise analysis for Lévy processes. Coauthors: Bernt Øksendal and Frank Proske (University of Oslo). Journal of Functional Analysis 206 (2004), 109-148.

59. Random Fields Evolution: non-anticipating integration and differentiation. Theory of Probability and Mathematical Statistics 66 (2002), 82-94; AMS 66 (2003), 91-104.

60. Explicit representation of the minimal variance portfolio in markets driven with Lévy processes. Coauthors: Fred Espen Benth, Arne Løkka, Bernt Øksendal, and Frank Proske (University of Oslo). Mathematical Finance 13 (2003), 55-72.

61. Stochastic integral representation, stochastic derivatives and minimal variance hedging. Stochastics and Stochastics Reports 73 (2002), 181-198.

62. Theory and numerical analysis for exact distributions of functionals of a Dirichlet process. Coauthors: Alessandra Guglielmi (CNR - Milano) and Eugenio Regazzini (University of Pavia). Annals of Statistics 30 (2002), 1376-1411.

63. Holder equality for conditional expectations with application to linear monotone operators. Theory of Probability and its Applications 48 (2003), 194-198; SIAM 48 (2004), 177-181.

64. On stochastic integration and differentiation. Coauthor: Yuri A. Rozanov (CNR - Milano). Acta Applicandae Mathematica  58 (1999), 231-235.

65. On measurable modification of stochastic functions. Coauthor: Yuri A. Rozanov (CNR - Milano). Theory of Probability and its Applications 46 (2001), 175-180; SIAM 46 (2002), 122-127.

Miscellanea

Technical reports

1. Kyle-Back’s model with Lévy noise (with José Manuel Corcuera, Gergely Farkas, and Bernt Øksendal), 2010. http://urn.nb.no/URN:NBN:no-28085

2. Random Fields: Skorohod integral and Malliavin derivative. Preprint Series in Pure Mathematics, University of Oslo, 36, 2004. ISSN 0806-2439.

3. On some versions of the fundamental theorem of asset pricing. Preprint Series in Pure Mathematics, University of Oslo, 14, 2002. ISBN 82-553-1334-6. 

4. On stochastic differentiation. Quaderno IAMI 99.23, CNR - Milano.

5. On monotone versions of Hahn-Banach extension theorem” (with Yu.A. Rozanov). Quaderno IAMI 99.11, CNR - Milano.

Collections

1. Stochastic differentiation and application to minimal variance hedging. Chapter 11 in Proceedings to the 4th Symposium on Lévy Processes: Theory and Applications. Manchester 13-15, 2005. 

2. Differenziazione stocastica non-anticipativa e applicazione alle coperture a varianza minima. Bollettino UMI Sezione A (December) 2004. Pages 491-495. Special Volume. (In Italian).

Theses

Ph.D. Thesis

“On Stochastic Differentiation with Application to Minimal Variance Hedging”. Dottorato di Ricerca in Statistica Matematica, Università degli Studi di Pavia, Italy (2002).

Thesis

“Measurability and Integrability of Stochastic Functions" (in Italian). Laurea in Matematica, Università degli Studi di Milano, Italy (1998).