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Fractional calculus and continuous-time finance

Citations

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Cited by:

  1. Valentina V. Tarasova & Vasily E. Tarasov, 2016. "Fractional Dynamics of Natural Growth and Memory Effect in Economics," Papers 1612.09060, arXiv.org, revised Jan 2017.
  2. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2009. "Correlated continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1194-1202, May.
  3. Hayashi, Katsuhiko & Kaizoji, Taisei & Pichl, Lukáš, 2007. "Correlation patterns of NIKKEI index constituents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 16-21.
  4. repec:eee:ejores:v:267:y:2018:i:2:p:765-777 is not listed on IDEAS
  5. repec:eee:apmaco:v:257:y:2015:i:c:p:52-65 is not listed on IDEAS
  6. Enrico Scalas & Rudolf Gorenflo & Hugh Luckock & Francesco Mainardi & Maurizio Mantelli & Marco Raberto, 2004. "Anomalous waiting times in high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 695-702.
  7. Scalas, Enrico & Politi, Mauro, 2012. "A parsimonious model for intraday European option pricing," Economics Discussion Papers 2012-14, Kiel Institute for the World Economy (IfW).
  8. Straka, P. & Henry, B.I., 2011. "Lagging and leading coupled continuous time random walks, renewal times and their joint limits," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 324-336, February.
  9. repec:eee:matcom:v:148:y:2018:i:c:p:37-47 is not listed on IDEAS
  10. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
  11. Bertram, William K., 2008. "Measuring time dependent volatility and cross-sectional correlation in Australian equity returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3183-3191.
  12. Enrico Scalas, 2005. "Five Years of Continuous-time Random Walks in Econophysics," Papers cond-mat/0501261, arXiv.org.
  13. Meerschaert, Mark M. & Scalas, Enrico, 2006. "Coupled continuous time random walks in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 114-118.
  14. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
  15. Pagnini, Gianni, 2014. "Short note on the emergence of fractional kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 29-34.
  16. Berardi, Luca & Serva, Maurizio, 2005. "Time and foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 403-412.
  17. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
  18. Alvaro Cartea & Thilo Meyer-Brandis, 2007. "How Does Duration Between Trades of Underlying Securities Affect Option Prices," Birkbeck Working Papers in Economics and Finance 0721, Birkbeck, Department of Economics, Mathematics & Statistics.
  19. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
  20. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
  21. repec:eee:apmaco:v:323:y:2018:i:c:p:31-42 is not listed on IDEAS
  22. Scalas, Enrico & Viles, Noèlia, 2014. "A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 385-410.
  23. Fei Ren & Gao-Feng Gu & Wei-Xing Zhou, 2009. "Scaling and memory in the return intervals of realized volatility," Papers 0904.1107, arXiv.org, revised Aug 2009.
  24. Masoliver, Jaume & Montero, Miquel & Perello, Josep & Weiss, George H., 2006. "The continuous time random walk formalism in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 577-598, December.
  25. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
  26. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
  27. Zheng, G.H. & Wei, T., 2010. "Spectral regularization method for the time fractional inverse advection–dispersion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 37-51.
  28. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2009. "Detrended fluctuation analysis of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 433-440.
  29. repec:eee:phsmap:v:497:y:2018:i:c:p:139-153 is not listed on IDEAS
  30. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Concept of dynamic memory in economics," Papers 1712.09088, arXiv.org.
  31. Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006. "Growth and allocation of resources in economics: The agent-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.
  32. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
  33. Sazuka, Naoya & Inoue, Jun-ichi & Scalas, Enrico, 2009. "The distribution of first-passage times and durations in FOREX and future markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2839-2853.
  34. repec:eee:apmaco:v:319:y:2018:i:c:p:518-526 is not listed on IDEAS
  35. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Dynamic intersectoral models with power-law memory," Papers 1712.09087, arXiv.org.
  36. Tristan Fletcher & John Shawe-Taylor, 2013. "Multiple Kernel Learning with Fisher Kernels for High Frequency Currency Prediction," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 217-240, August.
  37. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
  38. Guglielmo D'Amico & Filippo Petroni, 2013. "Multivariate high-frequency financial data via semi-Markov processes," Papers 1305.0436, arXiv.org.
  39. Schumer, Rina & Baeumer, Boris & Meerschaert, Mark M., 2011. "Extremal behavior of a coupled continuous time random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(3), pages 505-511.
  40. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
  41. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
  42. Kuroda, Koji & Murai, Joshin, 2007. "Limit theorems in financial market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 28-34.
  43. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
  44. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825.
  45. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
  46. Guo, Gang & Chen, Bin & Zhao, Xinjun & Zhao, Fang & Wang, Quanmin, 2015. "First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 279-290.
  47. Hosseiny, Ali & Gallegati, Mauro, 2017. "Role of intensive and extensive variables in a soup of firms in economy to address long run prices and aggregate data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 51-59.
  48. Repetowicz, Przemysław & Richmond, Peter, 2004. "Modeling of waiting times and price changes in currency exchange data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 677-693.
  49. D’Amico, Guglielmo & Janssen, Jacques & Manca, Raimondo, 2009. "European and American options: The semi-Markov case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3181-3194.
  50. Tian, WenYi & Li, Can & Deng, Weihua & Wu, Yujiang, 2012. "Regularization methods for unknown source in space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 45-56.
  51. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
  52. Masanao Aoki, 2006. "Patterns of Non-exponential Growth of Macroeconomic Models: Two-parameter Poisson-Dirichlet Models," CIRJE F-Series CIRJE-F-449, CIRJE, Faculty of Economics, University of Tokyo.
  53. Bertram, William K., 2009. "Optimal trading strategies for Itô diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2865-2873.
  54. Mura, A. & Taqqu, M.S. & Mainardi, F., 2008. "Non-Markovian diffusion equations and processes: Analysis and simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5033-5064.
  55. Miccichè, S., 2016. "Understanding the determinants of volatility clustering in terms of stationary Markovian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 186-197.
  56. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
  57. Langlands, T.A.M., 2006. "Solution of a modified fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 136-144.
  58. David, S.A. & Machado, J.A.T. & Quintino, D.D. & Balthazar, J.M., 2016. "Partial chaos suppression in a fractional order macroeconomic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 55-68.
  59. Masanao Aoki, 2006. "Patterns of Non-exponential Growth of Macroeconomic Models: Two-parameter Poisson-Dirichlet Models (Forthcoming in "Rivista Internazionale di Scienze Sociali", cxv No.1, pp. 109-125, 2007. )," CARF F-Series CARF-F-085, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  60. Barbieri, Davide & Vivoli, Alessandro, 2005. "Long-range correlations in time series generated by time-fractional diffusion: A numerical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 190-198.
  61. Valentina V. Tarasova & Vasily E. Tarasov, 2016. "Economic Accelerator with Memory: Discrete Time Approach," Papers 1612.07913, arXiv.org, revised Jul 2017.
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