228
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Limit Order Books, Diffusion Approximations and Reflected SPDEs: From Microscopic to Macroscopic Models

, &
Pages 132-170 | Received 16 Apr 2020, Accepted 16 Apr 2020, Published online: 13 May 2020

References

  • Abergel, F., and A. Jedidi. 2013. “A Mathematical Approach to Order Book Modeling.” International Journal of Theoretical and Applied Finance 16: 1350025, 40. doi:10.1142/S0219024913500258.
  • Almgren, R., and N. Chriss. 2001. “Optimal Execution of Portfolio Transactions.” Journal of Risk Research 3 (2): 5–39. doi:10.21314/JOR.2001.041.
  • Bayer, C., U. Horst, and J. Qiu. 2017. “A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics.” Annals of Applied Probability 27 (5): 2753–2806. doi:10.1214/16-AAP1265.
  • Blanchet, J., and X. Chen. 2013. “Continuous-time Modeling of Bid-ask Spread and Price Dynamics in Limit Order Books.” arXiv Preprint, arXiv:1310.1103.
  • Bovier, A., and J. Černý. 2007. “Hydrodynamic Limit for the A+B→∅ Model.” Markov Processes And Related Fields 13: 543–564.
  • Cartea, A., R. Donnelly, and S. Jaimungal. 2018. “Enhancing Trading Strategies with Order Book Signals.” Applied Mathematical Finance 25 (1): 1–35. doi:10.1080/1350486X.2018.1434009.
  • Cont, R., and A. de Larrard. 2011. “Price Dynamics in a Markovian Limit Order Market.” SIAM Journal on Financial Mathematics 4: 1–25.
  • Cont, R., S. Stoikov, and R. Talreja. 2010. “A Stochastic Model for Order Book Dynamics.” Operations Research 58 (3): 549–563. doi:10.1287/opre.1090.0780.
  • Deng, S., and X. Gao. 2018. “Hydrodynamic Limit of Order Book Dynamics.” Probability in the Engineering and Informational Sciences 32 (1): 96–125. doi:10.1017/S0269964816000413.
  • Diop, A. 2003. “Sur la discrétisation et le comportement à petit bruit d’EDS multidimensionnelles dont les coefficients sont à dérivées singulières.” Doctoral dissertation, INRIA.
  • Donati-Martin, C., and E. Pardoux. 1993. “White Noise Driven SPDEs with Reflection.” Probability Theory and Related Fields 95 (1): 1–24. doi:10.1007/BF01197335.
  • Donnelly, R., and L. Gan. 2018. “Optimal Decisions in a Time Priority Queue.” Applied Mathematical Finance 25 (2): 107–147. doi:10.1080/1350486X.2018.1506257.
  • Ethier, S., and T. Kurtz. 1986. Markov Processes: Characterization and Convergence. Wiley Series in Probability and Statistics. New York: Wiley.
  • Gould, M., M. Porter, S. Williams, M. McDonald, D. Fenn, and S. Howison. 2013. “Limit Order Books.” Quantitative Finance 13 (11): 1709–1742. doi:10.1080/14697688.2013.803148.
  • Hambly, B., and J. Kalsi. 2019. “A Reflected Moving Boundary Problem Driven by Space-time White Noise.” Stochastic Partial Differential Equations: Analysis and Computations 7: 746–807.
  • Horst, U., and M. Paulsen. 2017. “A Law of Large Numbers for Limit Order Books.” Mathematics of Operations Research 42 (4): 1280–1312. doi:10.1287/moor.2017.0848.
  • Huang, W., C.-A. Lehalle, and M. Rosenbaum. 2015. “Simulating and Analyzing Order Book Data: The Queue-reactive Model.” Journal of the American Statistical Association 110 (509): 107–122. doi:10.1080/01621459.2014.982278.
  • Keller-Ressel, M., and M. Müller. 2016. “A Stefan-type Stochastic Moving Boundary Problem.” Stochastic Partial Differential Equations: Analysis and Computations 4: 746–790.
  • Kim, K., R. Sowers, and Z. Zheng. 2012. “A Stochastic Stefan Problem.” Journal of Theoretical Probability 25 (4): 1040–1080. doi:10.1007/s10959-011-0392-1.
  • Kruk, L. 2003. “Functional Limit Theorems for a Simple Auction.” Mathematics of Operations Research 28 (4): 716–751. doi:10.1287/moor.28.4.716.20519.
  • Kyle, A. 1985. “Continuous Auctions and Insider Trading.” Econometrica 53 (6): 1315–1335. doi:10.2307/1913210.
  • Lakner, P., J. Reed, and S. Stoikov. 2016. “High Frequency Asymptotics for the Limit Order Book.” Market Micro Liquidity 2: 165004.
  • Mendelson, H. 1982. “Market Behavior in a Clearing House.” Econometrica 50 (6): 1505–1524. doi:10.2307/1913393.
  • Müller, M. 2016. “A Stochastic Stefan-type Problem under First Order Boundary Conditions.” Annals of Applied Probability 28 (4), 2335-2369.
  • Muni Toke, I. 2015. “The Order Book as a Queueing System: Average Depth and Influence of the Size of Limit Orders.” Quantitative Finance 15 (5): 795–808. doi:10.1080/14697688.2014.963654.
  • Roşu, I. 2019. “Liquidity and Information in Order Driven Markets.” SSRN Electronic Journal. https://ssrn.com/abstract=1286193
  • Tanaka, H. 1979. “Stochastic Differential Equations with Reflecting Boundary Condition in Convex Regions.” Hiroshima Mathematical Journal 9 (1): 163–177. doi:10.32917/hmj/1206135203.
  • Xu, T., and T. Zhang. 2009. “White Noise Driven SPDEs with Reflection: Existence, Uniqueness, and Large Deviation Principles.” Stochastic Processes and Their Applications 119 (10): 3453–3470. doi:10.1016/j.spa.2009.06.005.
  • Zhang, T. 2016. “Lattice Approximations of Reflected Stochastic Partial Differential Equations Driven by Space-Time White Noise.” Annals of Applied Probability 26 (6): 3602–3629. doi:10.1214/16-AAP1186.
  • Zheng, Z. 2012. “Stochastic Stefan Problems: Existence, Uniqueness and Modeling of Market Limit Orders.” PhD thesis, Graduate College of the University of Illinois at Urbana-Champaign.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.