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From Market Data to Agent-Based Models and Stochastic Differential Equations

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From Particle Systems to Partial Differential Equations III

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 162))

Abstract

A survey of results from 2008 to 2014 on the construction of a stochastic market model, from the empirical data to its modelling interpretation and proof of mathematical consistency (no-arbitrage and completeness).

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References

  1. Föllmer, H., Schied, A.: Stochastic Finance: An Introduction in Discrete Time. Walter de Gruyter, New York (2004)

    Book  MATH  Google Scholar 

  2. Gerardi, G.S., Lehnert, S., Sherland, S.M., Willen, P.S.: Making sense of the subprime crisis, Working paper 2009-2, Federal Bank of Atlanta

    Google Scholar 

  3. Mendes, R.V., Oliveira, M.J.: A data-reconstructed fractional volatility model, E-Economics/discussion paper/2008-22

    Google Scholar 

  4. Nualart, D.: The Malliavin Calculus and Related Topics. Springer, Berlin (2006)

    MATH  Google Scholar 

  5. Mendes, R.V., Oliveira, M.J., Rodrigues, A.M.: No-arbitrage, leverage and completeness in a fractional volatility model. Phys. A: Stat. Mech. Appl. 419, 470–478 (2015)

    Google Scholar 

  6. Björk, T.: Arbitrage Theory in Continuous Time. Oxford University Press, New York (2009)

    MATH  Google Scholar 

  7. Mendes, R.V.: A fractional calculus interpretation of the fractional volatility model. Nonlinear Dyn. 55, 395–399 (2009)

    Google Scholar 

  8. Rogers, L.C.G.: Arbitrage with fractional Brownian motion. Math. Finance 7, 95–105 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Shiryaev, A.N.: On arbitrage and replication for fractal models, Research Report 20. Department of Mathematical Sciences, University of Aarhus, Denmark, MaPhySto (1998)

    Google Scholar 

  10. Salopek, D.M.: Tolerance to arbitrage. Stochast. Process. Appl. 76, 217–230 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sottinen, T.: Fractional Brownian motion, random walks and binary market models. Finance Stochast. 5, 343–355 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cheridito, P.: Arbitrage in fractional Brownian motion models. Finance Stochast. 7, 533–553 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Guasoni, P.: No arbitrage under transaction costs, with fractional Brownian motion and beyond. Math. Finance 16, 569–582 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hu, Y., Øksendal, B.: Fractional white noise calculus and applications to finance. Infinite Dimensional Anal. Quantum Probab. Relat. Top. 6, 1–32 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Elliott, R.J., van der Hoek, J.: A general fractional white noise theory and applications to finance. Math. Finance 13, 301–330 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Björk, T., Hult, H.: A note on Wick products and the fractional Black-Scholes model. Finance Stochast. 9, 197–209 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mendes, R.V.: The fractional volatility model: an agent-based interpretation. Phys. A: Stat. Mech. Appl. 387, 3987–3994 (2008)

    Google Scholar 

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Correspondence to R. Vilela Mendes .

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Mendes, R.V. (2016). From Market Data to Agent-Based Models and Stochastic Differential Equations. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations III. Springer Proceedings in Mathematics & Statistics, vol 162. Springer, Cham. https://doi.org/10.1007/978-3-319-32144-8_11

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